Search Results (101)

This paper focuses on a high-order Korteweg–de Vries wave equation. The extended F-expansion method, a modified form of Kudryashov’s auxiliary equation approach, is employed to construct Jacobi elliptic function solutions for this equation. Three distinct families of solutions are obtained, including solitary waves, breathers, dark/bright solitons, bright–dark interaction solitons, and rogue-like solutions. To better illustrate the complex nonlinear dynamics of the high-order Korteweg–de Vries wave equation, representative solutions are selected, and their moduli are visualized using Maple software through three-dimensional, two-dimensional, and contour plots. Full article

Rogue waves are sudden, extreme events that pose a threat to offshore structures’ safety. Accurately replicating nonlinear rogue waves in laboratory settings is challenging but crucial for evaluating extreme loads. Recently, the time-reversal (TR) method based on the time-reversal feature of nonlinear water wave equations, such as the cubic Schrödinger equation, has shown breakthroughs in experimental rogue wave generation. However, when generating rogue waves of large steepness and strong nonlinearity (especially high-order rogue waves), this method encounters issues such as significantly insufficient wave height and weakened nonlinear characteristics. In this article, a modified time-reversal (MTR) method is proposed based on the dynamic transfer function between the rogue wave surface history and the motion of the wave-generator paddle. MTR adopts a two-round (just like TR) but seven-step procedure for high-order rogue wave generation. Using MTR, high-order rogue waves with respect to 1st–5th-order Peregrine breathers are successfully generated in a physical wave flume. Analysis of shape indices and the energy spectrum shows that MTR greatly improves the quality of high-order rogue wave generation over the TR method. It does this by increasing the focused wave height, improving wave profile accuracy, and better preserving the highly nonlinear features of rogue waves. Using the proposed MTR method, a fifth-order rogue wave was generated with a maximum steepness of 0.03. This exceeds previous studies, where the maximum wave steepness was typically around 0.01. Consequently, this work nearly triples the wave steepness compared to earlier results, yielding the steepest fifth-order rogue wave observed in water wave research. Full article

In this work, we examine the prospects of matching the Kadomtsev–Petviashvili (pKP) equation with the B-type Kadomtsev–Petviashvili (BKP) equation, which we will call the pKP-BKP equation. The resulting model gives a rigorous mathematical framework for describing long wave phenomena in oceans, impoundments and estuaries and for forecasting tsunamis; river, tide and irrigation flows; and wave patterns in the atmosphere. Using a consolidated method of analysis based on symmetry reductions and rational function transformations, we obtain several classes of exact solutions composed of rational, periodic, breather and kink-wave structures. These methods shed light on the interplay between symmetries that control the formation of soliton solutions, hence allowing the construction of new families of analytical soliton solutions. The solutions obtained are linked together through spectral degeneracies and reductions in symmetry. These methodologies are presented in a systematic way, emphasizing their applicability to a general class of nonlinear evolution equations. The results of the analysis are substantiated through direct substitution, and the structural characteristics of the solutions are discussed in detail. As a result, these results expand the solution space of the pKP–BKP equation and provide better analytical insights into Kadomtsev–Petviashvili-type nonlinear evolution equations. Full article

This paper presents the construction of exact wave solutions for the generalized nonlinear Schrödinger equation (NLSE) with second-order spatiotemporal dispersion using the modified exponential rational function method (mERFM). The NLSE plays a vital role in various fields such as quantum mechanics, oceanography, transmission lines, and optical fiber communications, particularly in modeling pulse dynamics extending beyond the traditional slowly varying envelope estimation. By incorporating higher-order dispersion and nonlinear effects, including cubic–quintic nonlinearities, this generalized model provides a more accurate representation of ultrashort pulse propagation in optical fibers and oceanic environments. A wide range of soliton solutions is obtained, including bright and dark solitons, as well as trigonometric, hyperbolic, rational, exponential, and singular forms. These solutions offer valuable insights into nonlinear wave dynamics and multi-soliton interactions relevant to shallow- and deep-water wave propagation. Conservation laws associated with the model are also derived, reinforcing the physical consistency of the system. The stability of the obtained solutions is investigated through the analysis of modulation instability (MI), confirming their robustness and physical relevance. Graphical representations based on specific parameter selections further illustrate the complex dynamics governed by the model. Overall, the study demonstrates the effectiveness of mERFM in solving higher-order nonlinear evolution equations and highlights its applicability across various domains of physics and engineering. Full article

In the current paper, we study breather propagation and arrest in chains with significantly nonlinear interactions of elements depending on the type of nonlinearity. We extend the consideration of the two-stage propagation of breathers in these chains on the relevant substrates to the general case of power-law nonlinear nearest-neighbor interaction. Our work concerns the effect of the nonlinearity on breather propagation and breather arrest. We exploit the simplified model to predict the main features of breather arrest for a wide range of nonlinearity types, including smooth-function analogs for vibro-impact contact. Full article

In this work, we study a generalised high-order nonlinear Schrödinger equation with time-dependent coefficients, embracing a wide range of physical influences. By employing the Darboux transformation, we construct explicit breather and rogue wave solutions, illustrating how the spectral parameter governs waveform transitions. In these dynamics, dispersion determines stability and symmetry, nonlinearity influences the peak amplitude and width, and third-order dispersion introduces asymmetry and drift in the wave profile. We have demonstrated that stabilization, destabilization and shifting of the centre of the localization, or drifting towards the soliton in space or even temporal directions, can be possible by manoeuvring the spectral parameter relating dispersion and nonlinearity in optical fibre. Manoeuvring the spectral parameter relates the dispersion $a_1\left(t\right)$ and nonlinearity from 100 t to 0.1 t leads to the stabilization of the soliton by a notable decrease in the amplitude for two hundred folds. The results reveal that the inclusion of higher-order term functions as a control mechanism for managing instability and localisation in nonlinear optical fibre systems, offering promising prospects for future developments in nonlinear optics. Full article

Background/Objectives: Maxillary transverse deficiency is linked to impaired nasal breathing and pediatric sleep-disordered breathing. This systematic review evaluated the effects of maxillary expansion (ME) on upper-airway morphology and breathing function in growing patients. Methods: The search was conducted on PubMed/MEDLINE, Scopus, ScienceDirect, Cochrane CENTRAL, and gray literature (January 2015–April 2025). Eligible RCTs, controlled trials, and cohort/observational studies assessed airway morphology and/or respiratory outcomes after ME in pediatric/adolescent patients. Risk of bias was evaluated with RoB 2 (RCTs) and ROBINS-I (non-randomized studies). The findings were synthesized qualitatively and certainty graded with GRADE. Results: Forty-one studies were included. Imaging consistently showed enlargement of the nasal cavity and nasopharynx after expansion, whereas the effects in the oropharynx and hypopharynx, as well as in the maxillary sinuses, were smaller or variable. Objective patency improved in several studies (higher peak nasal inspiratory flow, reduced nasopharyngeal obstruction, and nasal resistance), whereas computational fluid dynamics generally showed non-significant trends toward lower resistance. Spirometry improved, particularly in oral breathers (gains in FEV₁, FVC, FEF25–75%). Polysomnography indicated reductions in AHI and improved oxygenation in some pediatric OSA cohorts, although other RCTs reported null PSG effects. Caregiver-reported sleep and quality-of-life outcomes were consistently enhanced. Device design modestly influenced regional widening, but overall respiratory effects were similar across expanders. By GRADE, certainty was low for airway morphology and very low for breathing function. Conclusions: In growing patients, ME reliably enlarges upper-airway compartments, especially the nasal cavity and nasopharynx, yet functional improvements are heterogeneous. Standardized outcomes and integrated morphological–functional assessments are needed to strengthen the evidence base. Full article

Introduction/Goal: Stress and negative emotions have been shown to exert a substantial impact on cancer patients, affecting their ability to adapt to therapy and the overall effectiveness. Elevated cortisol levels, a stress-induced hormone, have been shown to suppress immune system function, potentially reducing the body’s capacity to combat cancer cells. On the contrary, prolactin, a hormone that stimulates the immune system, has shown potential in this context but requires further study. The objective of this study was to investigate the acute physiological changes that occur during a single Conscious Connected Breathing (CCB) session, as part of a larger investigation on Integrative Breathwork Psychotherapy (IBP), a novel integrative psychosomatic intervention designed to improve psychosomatic and immune status in cancer patients. Methods: The project involved 93 breast cancer patients hospitalized for postoperative radiotherapy who participated in a ten-session IBP program. Fifty-six patients agreed to participate (response rate: 60%). During the experiment, 8 patients were excluded from the analysis. IBP consisted of small group sessions (up to six participants) conducted three times weekly. Each session included 45 min of CCB—defined as rhythmic circular nasal breathing at a depth exceeding resting tidal volume, without breath-holding, performed in a state of mindful acceptance—followed by 15 min of free emotional expression (verbal articulation of emerging feelings and sensations). This was a within-subject pre-post design: physiological measurements were obtained immediately before and 30 min into the tenth session (when participants had achieved technical proficiency) in all participants, who served as their own controls. Outcome measures included: arterialized capillary blood gas parameters (pH, pCO₂, pO₂, ctO₂, COHb, HHb, cH⁺), serum cortisol and prolactin concentrations, and immunoglobulin A (IgA). Results: During the CCB session, blood gas analysis revealed significant changes consistent with mild respiratory alkalosis: decreases in pCO₂ (p = 0.003), pO₂ (p < 0.001), cH⁺ (p < 0.001), ctO₂ (p < 0.001), COHb (p = 0.03), and HHb (p = 0.004), alongside an increase in pH (p < 0.001). Concurrently, prolactin levels increased significantly (p < 0.001), while cortisol (p < 0.001) and IgA (p < 0.001) decreased. Conclusions: This study is the first to analyze acute changes in capillary blood gas parameters and neuroendocrine balance during Conscious Connected Breathing sessions in cancer patients, revealing measurable immunostimulatory and stress-modulatory effects. The observed shift toward respiratory alkalosis, combined with increased prolactin and decreased cortisol, suggests that CCB may facilitate favorable neuroendocrine-immune interactions. These findings support the potential of breathwork as a complementary therapy for cancer patients. Further research is needed to explore underlying mechanisms and assess long-term psychological and immunological impacts. Full article

In this study, we consider a (2+1)-dimensional integrable Boussinesq equation, where the Hirota method of positive logarithmic transformation is used to convert it into a bilinear form. We proceeded by employing different test functions, through which we obtained breather solutions, two-wave solutions, lump-periodic solutions, and new interaction solutions. The resulting soliton dynamics for the governing model are also derived using the enhanced modified extended tanh function method, where varieties of solutions, such as trigonometric, hyperbolic, and rational forms, were obtained. The derived solutions may hold significant potential for explaining real-world physical phenomena in fields like mathematical physics, plasma physics, and nonlinear optics. The accuracy and reliability of the solutions were tested by substituting them back into the original equation using Python, highlighting the method’s robustness, precision, and reliability. By choosing appropriate physical parameters, we showcased the rich diversity and dynamic behavior of the obtained soliton structures. In other words, the graphical representations in 3D, contour, and 2D were provided for some of the obtained results. The modulation instability analysis and gain spectrum of the model are also provided. The importance of the obtained results in the area of (2+1)-dimensional integrable equation application was also highlighted. Full article

This study examines the soliton dynamics in the time-fractional cubic–quintic nonlinear non-paraxial propagation model, applicable to optical signal processing, nonlinear optics, fiber-optic communication, and biomedical laser–tissue interactions. The fractional framework exhibits a wide range of nonlinear effects, such as self-phase modulation, wave mixing, and self-focusing, arising from the balance between cubic and quintic nonlinearities. By employing the Multivariate Generalized Exponential Rational Integral Function (MGERIF) method, we derive an extensive catalog of analytic solutions, multi-peakon structures, lump solitons, kinks, and bright and dark solitary waves, while periodic and singular solutions emerge as special cases. These outcomes are systematically constructed within a single framework and visualized through 2D, 3D, and contour plots under both anomalous and normal dispersion regimes. The analysis also addresses modulation instability (MI), interpreted as a sideband amplification of continuous-wave backgrounds that generates pulse trains and breather-type structures. Our results demonstrate that cubic–quintic contributions substantially affect MI gain spectrum, broadening instability bands and permitting MI beyond the anomalous-dispersion regime. These findings directly connect the obtained solution classes to experimentally observed routes for solitary wave shaping, pulse propagation, and instability and instability-driven waveform formation in optical communication devices, photonic platforms, and laser technologies. Full article

Background/Objectives: The hyoid bone plays a central role in functions such as swallowing, speech, and airway maintenance, and its morphology may vary with anatomical and functional parameters. This study aimed to evaluate the influence of skeletal class, respiratory mode, age, and sex on the morphometric features of the hyoid bone using cone-beam computed tomography (CBCT). Methods: A total of 560 CBCT scans (295 females, 265 males; aged 8–73 years) were retrospectively analyzed. Hyoid angle, horizontal length, and vertical height were measured using Dolphin 3D software. Participants were categorized by skeletal class (I, II, III), breathing pattern (nasal vs. oral), and age group. Data were analyzed using robust three-way ANOVA and Bonferroni post hoc tests. Results: In females, nasal breathers exhibited significantly larger hyoid angles and vertical heights than oral breathers (p < 0.001), independent of age and skeletal class. In males, both age and breathing mode significantly influenced hyoid angle and vertical length (p < 0.001). Vertical height was also significantly greater in skeletal Class I compared to Class III (p = 0.008). Notably, significant respiration–skeletal class interaction was found in females (p = 0.029) but not in males. Conclusions: Hyoid bone morphology is affected by age, breathing pattern, and skeletal class, with sex-specific differences. Nasal breathing and younger age were associated with more inferior and angularly favorable hyoid positions, which may have implications for airway stability and craniofacial development. Full article

We derive a new exactly solvable multi-component system of non-linear evolution equations (NLEEs). The system consists of three $1+1$-dimensional evolution equations—one first-order and two second-order in the spatial variable. We review their Lax representation, formulate the scattering problem, and derive the soliton-like solutions of the system. Full article

In this study, we investigate the fractional Tzitzéica equation, a nonlinear evolution equation known for modeling complex phenomena in various scientific domains such as solid-state physics, crystal dislocation, electromagnetic waves, chemical kinetics, quantum field theory, and nonlinear optics. Using the (G′/G, 1/G)-expansion approach, we derive different categories of exact solutions, like hyperbolic, trigonometric, and rational functions. The beta fractional derivative is used here to generalize the classical idea of the derivative, which preserves important principles. The derived solutions with broader nonlinear wave structures are periodic waves, breathers, peakons, W-shaped solitons, and singular solitons, which enhance our understanding of nonlinear wave dynamics. In relation to these results, the findings are described by showing the solitons’ physical behaviors, their stabilities, and dispersions under fractional parameters in the form of contour plots and 2D and 3D graphs. Comparisons with earlier studies underscore the originality and consistency of the (G′/G, 1/G)-expansion approach in addressing fractional-order evolution equations. It contributes new solutions to analytical problems of fractional nonlinear integrable systems and helps understand the systems’ dynamic behavior in a wider scope of applications. Full article

This paper investigates the bifurcation dynamics and optical soliton solutions of the integrable quintic Kundu–Eckhaus (QKE) equation with an M-fractional derivative. By adding quintic nonlinearity and higher-order dispersion, this model expands on the nonlinear Schrödinger equation, which makes it especially applicable in explaining the propagation of high-power optical waves in fiber optics. To comprehend the behavior of the connected dynamical system, we categorize its equilibrium points, determine and analyze its Hamiltonian structure, and look at phase diagrams. Moreover, integrating along periodic trajectories yields soliton solutions. We achieve this by using the simplest equation approach and the modified extended Tanh method, which allow for a thorough investigation of soliton structures in the fractional QKE model. The model provides useful implications for reducing internet traffic congestion by including fractional temporal dynamics, which enables directed flow control to avoid bottlenecks. Periodic breather waves, bright and dark kinky periodic waves, periodic lump solitons, brilliant-dark double periodic waves, and multi-kink-shaped waves are among the several soliton solutions that are revealed by the analysis. The establishment of crucial parameter restrictions for soliton existence further demonstrates the usefulness of these solutions in optimizing optical communication systems. The theoretical results are confirmed by numerical simulations, highlighting their importance for practical uses. Full article

This study sought to deepen our understanding of the dynamical properties of the newly extended $(3+1)$-dimensional integrable Kadomtsev–Petviashvili (KP) equation, which models the behavior of ion acoustic waves in plasmas and nonlinear optics. This paper aimed to perform Lie symmetry analysis and derive lump, breather, and soliton solutions using the extended hyperbolic function method and the generalized logistic equation method. It also analyzed the dynamical system using chaos detection techniques such as the Lyapunov exponent, return maps, and the fractal dimension. Initially, we focused on constructing lump and breather soliton solutions by employing Hirota’s bilinear method. Secondly, employing Lie symmetry analysis, symmetry generators were utilized to satisfy the Lie invariance conditions. This approach revealed a seven-dimensional Lie algebra for the extended $(3+1)$-dimensional integrable KP equation, incorporating translational symmetry (including dilation or scaling) as well as translations in space and time, which were linked to the conservation of energy. The analysis demonstrated that this formed an optimal sub-algebraic system via similarity reductions. Subsequently, a wave transformation method was applied to reduce the governing system to ordinary differential equations, yielding a wide array of exact solitary wave solutions. The extended hyperbolic function method and the generalized logistic equation method were employed to solve the ordinary differential equations and explore closed-form analytical solitary wave solutions for the diffusive system under consideration. Among the results obtained were various soliton solutions. When plotting the results of all the solutions, we obtained bright, dark, kink, anti-kink, peak, and periodic wave structures. The outcomes are illustrated using 2D, 3D, and contour plots. Finally, upon introducing the perturbation term, the system’s behavior was analyzed using chaos detection techniques such as the Lyapunov exponent, return maps, and the fractal dimension. The results contribute to a deeper understanding of the dynamic properties of the extended KP equation in fluid mechanics. Full article