In this study, the Lie group method for constructing exact and numerical solutions of the generalized time-dependent variable coefficients Burgers’, Burgers’–KdV, and KdV equations with initial and boundary conditions is presented. Lie group theory i...
The KdV equation has many applications in mechanics and wave dynamics. Therefore, researchers are carrying out work to develop and analyze modified and generalized forms of the standard KdV equation. In this paper, we inspect the KdV-mKdV equation, w...
We extend two KdVSKR models to fractional KdVSKR models with the Caputo derivative. The KdVSKR equation in (2+1)-dimension, which is a recent extension of the KdVSKR equation in (1+1)-dimension, can model the soliton resonances in shallow water. Appl...
The most well-known equations both in the theory of nonlinearity and dispersion, KdV equations, have received tremendous attention over the years and have been used as model equations for the advancement of the theory of solitons. In this paper, some...
Background: While Bacillus Calmette-Guérin (BCG) remains the first-line therapy for high-risk bladder cancer, 30–40% of patients develop treatment resistance necessitating radical cystectomy, some are not suitable candidates for this pro...
KD025, a ROCK2 isoform-specific inhibitor, has an anti-adipogenic activity which is not mediated by ROCK2 inhibition. To identify the target, we searched binding targets of KD025 by using the KINOMEscanTM screening platform, and we identified casein...
The white-noise-driven KdV-type Boussinesq system is a class of stochastic partial differential equations (SPDEs) that describe nonlinear wave propagation under the influence of random noise—specifically white noise—and generalize feature...
In this Letter, the (G'/G) -expansion method is proposed to seek exact solutions of nonlinear evolution equations. For illustrative examples, we choose the compound KdV-Burgers equation, the compound KdV equation, the KdV-Burgers equation, the mKdV e...
Here, we analyze the (2+1)-dimensional stochastic modified Kordeweg–de Vries (SmKdV) equation perturbed by multiplicative white noise in the Stratonovich sense. We apply the mapping method to obtain new trigonometric, elliptic, and rational sto...
The general variable coefficient cylindrical/spherical KdV equation has been investigated by using the simplified homogeneous balance method. It has been proven that if its coefficients satisfy certain constraint conditions, then the cylindrical/sphe...
From the finite gap solutions of the KdV equation expressed in terms of abelian functions we construct solutions to the Schrödinger equation with a KdV potential in terms of fourfold Fredholm determinants. For this we establish a connection betw...
The multi-symplectic integrator, as a numerical integration approach with symmetry, is known to have the characteristic of preserving the qualitative features and geometric properties of certain systems. Using the multi-symplectic integrator, the num...
In this paper, we establish exact solutions for the non-linear coupled KdV equations. The exp-function method is used to construct the solitary travelling wave solutions for these equations. The numerical adaptive moving mesh PDEs (MMPDEs) method is...
In this paper, we propose two efficient methods for solving the fractional-order Schrödinger–KdV system. The first method is the Laplace residual power series method (LRPSM), which involves expressing the solution as a power series and usi...
In order to construct the multiple traveling wave solutions of the nonlocal modified Korteweg de Vires (mKdV) equation, the modified tanh-function approach for local soliton equations is extended to a nonlocal complex mKdV equation. The central idea...
Cryptography is the science and study of protecting data in computer and communication systems from unauthorized disclosure and modification. An ordinary difference equation (a map) can be used in encryption–decryption algorithms. In particular, the...
Eye movement disorders have been reported in patients with multiple sclerosis (MS) as saccadic disturbances. Several methods have been described for the assessment of saccades, including the K-D and DEM tests. The performance of these tests also invo...
In this paper, numerical solutions of the variable-coefficient Korteweg-De Vries (vcKdV) equation with space described by the Caputo fractional derivative operator is developed. The propagation and interaction of vcKdV equation in different cases, su...
In this paper, we studied the numerical solution of a time-fractional Korteweg–de Vries (KdV) equation with new generalized fractional derivative proposed recently. The fractional derivative employed in this paper was defined in Caputo sense and cont...
In this article, we investigate the generalized Kawahara–KdV system. A new topological approach is applied to prove the existence of at least one classical solution and at least two non-negative classical solutions. The arguments are based upon...
In the field of nonlinear mathematical physics, Ablowitz et al.’s algorithm has recently made significant progress in the inverse scattering transform (IST) of fractional-order nonlinear evolution equations (fNLEEs). However, the solved fNLEEs...
This paper explores the exact solutions of the fractional Hirota–Satsuma coupled KdV (fHScKdV) equation in the Beta fractional derivative. The logistic method is first proposed to construct analytical solutions for the fHScKdV equation. In orde...
Nonlinear science is a fundamental science frontier that includes research in the common properties of nonlinear phenomena. This article is devoted for the study of new extended hyperbolic function method (EHFM) to attain the exact soliton solutions...
This paper primarily concerns the Whitham modulation equation of the complex modified Korteweg–de Vries (cmKdV) equation with a step-like initial value. By utilizing the Lax pair, we derive the N-genus Whitham equations via the averaging method...
Background/Objectives: Respiratory syncytial virus (RSV) causes severe infection in neonates and infants. However, a suitable RSV vaccine for children is yet to be approved. The development of KD-409 is focused on creating an effective and safe RSV v...
To overcome incomplete point cloud data obtained from laser scanners scanning complex surfaces, multi-viewpoint cloud data needs to be aligned for use. A hybrid improved SAC-IA with a KD-ICP algorithm is proposed for local point cloud alignment optim...
KdV equations have a lot of applications of in fluid mechanics. The exact solutions of the KdV equations play a vital role in the wave dynamics of fluids. In this paper, some new exact solutions of a generalized geophysical KdV equation are computed...
KD025 (SLx-2119), the first specific Rho-associated protein kinase 2 (ROCK2) inhibitor, is a potential new drug candidate currently undergoing several phase 2 clinical trials for psoriasis, idiopathic pulmonary fibrosis, chronic graft-versus-host dis...
This research work is dedicated to solving the n-generalized Korteweg–de Vries (KdV) equation in a fractional sense. The method is a combination of the Sumudu transform and the Adomian decomposition method. This method has significant advantage...
The main features of scientific efforts in physics and engineering are the development of models for various physical issues and the development of solutions. In order to solve the time-fractional coupled Korteweg–De Vries (KdV) equation, we co...
The fractional Schrödinger–Korteweg-de Vries (S-KdV) equation is an important mathematical model that incorporates the nonlinear dynamics of the KdV equation with the quantum mechanical effects described by the Schrödinger equation. M...
Bayesian inference using Gaussian processes on large datasets have been studied extensively over the past few years. However, little attention has been given on how to apply these on a high resolution input space. By approximating the set of test poi...
A critical parameter to assess the environmental status of water bodies is the transparency of the water, as it is strongly affected by different water quality related components (such as the presence of phytoplankton, organic matter and sediment con...
We consider the negative order KdV (NKdV) hierarchy which generates nonlinear integrable equations. Selecting different seed functions produces different evolution equations. We apply the traveling wave setting to study one of these equations. Assumi...
The (2+1)-dimensional fifth-order KdV equation and (2+1)-dimensional Gardner equation obtained by us using Euler equations for an ideal fluid model in 2023 are revisited. Including additional second-order corrections enabled the derivation of the (2+...
Forest fire detection is an essential application in environmental surveillance since wildfires cause devastating damage to ecosystems, human life, and property every year. The effective and accurate detection of fire is necessary to allow for timely...
In analysis of problems with parametric spline boundaries that are immersed or inserted into an underlying domain, the discretization on the underlying domain usually does not conform to the inserted boundaries. While the fixed underlying discretizat...
The stochastic fractional-space Korteweg–de Vries equation (SFSKdVE) in the sense of the M-truncated derivative is examined in this article. In the Itô sense, the SFSKdVE is forced by multiplicative white noise. To produce new trigonometr...
This article extends the celebrated Riemann–Hilbert (RH) method equipped with mixed spectrum to a new integrable system of three-component coupled time-varying coefficient complex mKdV equations (ccmKdVEs for short) generated by the mixed spect...
In this article, we discuss the (2 + 1)-D coupled Korteweg–De Vries (KdV) equations whose coefficients are variables, and stochastic (2 + 1)-D C-KdV (C-KdV) equations with the χ-Wick-type product. White noise functional solutions (WNFS) are...
The simulation of wave propagation, such as soliton propagation, based on the Rosenau-KdV-RLW equation on unbounded domains requires a bounded computational domain. Therefore, a special boundary treatment, such as an absorbing boundary condition (ABC...
This paper explores the reverse space-time mKdV equation through the application of the Riemann–Hilbert problem. Under the zero boundary condition, we derive the Jost solutions, examine their the analytic and symmetry properties alongside those...
This paper considers the transformation of a sine wave in the framework of the extended modified Korteweg–de Vries equation or (2+4) KdV, which includes a combination of cubic and quintic nonlinearities. It describes the internal waves in a med...
The KdV equation has special significance as it describes various physical phenomena. In this paper, we use two methods, namely, a variational homotopy perturbation method and a classical finite-difference method, to solve 1D and 2D KdV equations wit...
In this study, we build multi-wave solutions of the KdV-5 model through Hirota’s bilinear method. Taking complex conjugate values of the free parameters, various colliding exact solutions in the form of rogue wave, symmetric bell soliton and ro...
The exact traveling wave solutions to coupled KdV equations with variable coefficients are obtained via the use of quadratic Jacobi’s elliptic function expansion. The presented coupled KdV equations have a more general form than those studied i...
Two numerical methods are investigated for the initial–boundary value problem of a nonlinear Rosenau–KdV–RLW equation with homogeneous boundary conditions. With the premise of achieving second-order theoretical accuracy in the tempo...
In this study, we applied the Laplace residual power series method (LRPSM) to expand the solution of the nonlinear time-fractional coupled Hirota–Satsuma and KdV equations in the form of a rapidly convergent series while considering Caputo frac...
For the rapid, reliable, and cost-effective methods of tuberculosis (TB) auxiliary diagnosis, antibody (Ab) detection to multiple antigens of Mycobacterium tuberculosis (Mtb) has great potential; however, this methodology requires optimization. We co...
In this work, we study the bifurcation and the numerical analysis of the nonlinear Benjamin-Bona-Mahony-KdV equation. According to the bifurcation theory of a dynamic system, the various kinds of traveling wave profiles are obtained including the beh...
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