We determine the interaction energy of electric monopole pairs, sources and sinks of a Coulombic field. These charges are represented by topological solitons of finite size and mass, described by a field of SO(3) rotations without any divergences. Su...
Electromagnetically induced transparency (EIT) is well known as a quantum optical phenomenon that permits a normally opaque medium to become transparent due to the quantum interference between transition pathways. This work addresses multi-soliton dy...
In this paper, the Hirota bilinear method, which is an important scheme, is used. The equation of the shallow water wave in oceanography and atmospheric science is extended to (3+1) dimensions, which is a well-known equation. A lot of classes of rati...
Pairwise interactions of particle-like waves (such as solitons and breathers) are important elementary processes that play a key role in the formation of the rarefied soliton gas statistics. Such waves appear in different physical systems such as dee...
In this paper, Artificial Intelligence (AI) is developed for studying the Boussinesq Paradigm equation and so called b-equation based on Physics-Informed Cellular Neural Networks (PICNNs). The models studied here come from fluid dynamics. Machine lea...
Weak interactions of temporal cavity solitons resulting from gain saturation and recovery in a delay differential model of a long cavity semiconductor laser were studied numerically and analytically using an asymptotic approach. This paper shows that...
The reverse space-time nonlocal complex modified Kortewewg–de Vries (mKdV) equation is investigated by using the consistent tanh expansion (CTE) method. According to the CTE method, a nonauto-Bäcklund transformation theorem of nonlocal com...
Pair soliton interactions play a significant role in the dynamics of soliton turbulence. The interaction of solitons with different polarities is particularly crucial in the context of abnormally large wave formation, often referred to as freak or ro...
Solitons are self-trapped modes existing in various nonlinear systems. Creating stable solitons in two- and three-dimensional settings is a challenging goal in various branches of physics. Several methods have been developed theoretically and experim...
The capacity limits of fiber-optic communication systems in the nonlinear regime are not yet well understood. In this paper, we study the capacity of amplitude modulated first-order soliton transmission, defined as the maximum of the so-called time-s...
Benefiting from ultrafast temporal resolution, broadband spectral bandwidth, as well as high peak power, passively mode-locked fibre lasers have attracted growing interest and exhibited great potential from fundamental sciences to industrial and mili...
The (2+1)-dimensional integrable Caudrey–Dodd–Gibbon–Kotera–Sawada equation is a higher-order generalization of the Kadomtsev–Petviashvili equation, which can be applied in some physical branches such as the nonlinear di...
In this article, we consider the improved perturbed nonlinear Schrödinger Equation (IP-NLSE) with dual power law nonlinearity, which arises in optical fibers and photovoltaic-photo-refractive materials. We found grey and black optical solitons o...
In this paper, a dissipative version of the Benjamin–Ono dynamics is shown to faithfully model the collective evolution of swarms of scalar Cauchy stochastic agents obeying a follow-the-leader interaction rule. Due to the Hilbert transform, the...
We present an overview of multisoliton chains arising in various non-integrable field theories and discuss different mechanisms which may lead to the occurrence of such axially-symmetric classical solutions. We explain the pattern of interactions bet...
The influences of electromagnetic fields (EMFs) on bio-energy transport and its mechanism of changes are investigated through analytic and numerical simulation and experimentation. Bio-energy transport along protein molecules is performed by soliton...
Applying an imaginary time evolution method (AITEM) to the system of Gross–Pitaevskii equations, we find two-dimensional stable solitons in binary atomic Bose–Einstein condensates with spin–orbit coupling (SOC) and the Rydberg&ndash...
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...
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...
We investigate the interactions of in-phase Airy beams modulated by a fundamental Gaussian beam and fourth-order diffraction in Kerr nonlinear media. Directly numerical simulations show that normal (anomalous) fourth-order diffraction and an in-phase...
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 whic...
In this paper, soliton solutions, lump solutions, breather solutions, and lump-solitary wave solutions of a (2+1)-dimensional variable-coefficient extended shallow-water wave (vc-eSWW) equation are obtained based on its bilinear form. By calculating...
In this study, the evolution of surface water solitary waves under the action of Jeffreys’ wind–wave amplification mechanism in shallow water is analytically investigated. The analytic approach is essential for numerical investigations du...
Solitons are a challenging topic in condensed matter physics and materials science because of the interplay between their topological and physical properties and for the crucial role they play in topological phase transitions. Among them, chiral skyr...
Conventional soliton (CS) and noise-like pulse (NLP) are two different kinds of pulse regimes in ultrafast fiber lasers, which have many intense applications. In this article, we experimentally demonstrate that the pulse regime of an Er-doped fiber l...
The concept of ranked order probability distribution unveils natural probabilistic interpretations for the kink waves (and hence the solitons) solving higher order dispersive Burgers’ type PDEs. Thanks to this underlying structure, it is possib...
As an extension of the class of nonlinear PT -symmetric models, we propose a system of sine-Gordon equations, with the PT symmetry represented by balanced gain and loss in them. The equations are coupled by sine-field terms and first-order...
Optical solitons in ultrafast fiber lasers, as a result of dual balances between dispersion and nonlinearity as well as gain and loss, enable various soliton interactions. Soliton collisions are among the most intriguing soliton interactions, which f...
The generalized (2 + 1)-dimensional Date–Jimbo–Kashiwara–Miwa (gDJKM) equation, which can be used to describe some phenomena in fluid mechanics, is investigated based on the multi-soliton solution. Soliton molecules of the gDJKM equ...
We investigate the dynamics of vector solitons in a two-component Bose–Einstein condensates governed by the system of Gross–Pitaevskii equations. Using a gauge-transformation approach, we construct a four-soliton solution and analyze thei...
In this paper, we use the multilinear variable separation approach involving two arbitrary variable separation functions to construct a new variable separation solution of the (4+1)-dimensional Boiti–Leon–Manna–Pempinelli equation....
The parity-time symmetric nonlocal nonlinear Schrödinger equation with self-consistent sources (PTNNLSESCS) is used to describe the interaction between an high-frequency electrostatic wave and an ion-acoustic wave in plasmas. In this paper, the...
We present a simple model of interaction of the Maxwell equations with a matter field defined by the Klein–Gordon equation. A simple linear interaction and a nonlinear perurbation produces solutions to the equations containing hylomorphic solitons, n...
The propagation characteristics of a single Airy beam in nonlinear Kerr media were numerically investigated by utilizing the split-step Fourier transform method. We show that in addition to normal breathing solitons, the anomalous bound states of Air...
The existence, stability, and dynamics of bound pairs of symbiotic matter waves in the form of dark-bright soliton pairs in two-component mixtures of atomic Bose–Einstein condensates is investigated. Motivated by the tunability of the atomic interact...
Exciton–polariton condensates (EPCs) have emerged as a paradigmatic platform for investigating nonequilibrium quantum many-body phenomena, particularly due to their intrinsic open-dissipative nature and strong nonlinear interactions governed by...
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...
Numerical simulations were performed to study the long-distance evolution of irregular waves in deep water. It was observed that some solitons, which are the theoretical solutions of the nonlinear Schrödinger equation, emerged spontaneously as i...
The nonlinear dynamics of the interface between two immiscible dielectric liquids at the regime of suppressed Kelvin-Helmholtz instability by external horizontal electric field is studied theoretically. The initial equations of the fluids motion are...
This study focuses on the analysis of soliton solutions within the framework of the time-fractional cubic–quintic nonlinear Schrödinger equation (TFCQ-NLSE), a powerful model with broad applications in complex physical phenomena such as fi...
We study the reflection and transmission properties of matter wave solitons impinging on localized scattering potentials in one spatial dimension. By mean field analysis we identify regimes where the solitons behave more like waves or more like parti...
This paper aims to seek soliton solutions for the nonlocal generalized Sasa–Satsuma (gSS) equation by constructing the Darboux transformation (DT). We obtain soliton solutions for the nonlocal gSS equation, including double-periodic wave, breat...
The KP hierarchy reduction method is one of the most reliable and efficient techniques for determining exact solitary wave solutions to nonlinear partial differential equations. In this paper, according to the KP hierarchy reduction technique, ration...
A truncated M-fractional Kadomtsev–Petviashvili (KP) equation in high-dimensional space has been proposed. The model provides the oretical support for studying the interaction patterns among waves. According to the attributes of the truncated M...
We produce soliton and similarity solutions of supersymmetric extensions of Burgers, Korteweg–de Vries and modified KdV equations. We give new representations of the τ -functions in Hirota bilinear formalism. Chiral superfields are used to obtain suc...
Exploring the dynamics of a mobile impurity immersed in field excitations is challenging, as it requires to account for the entanglement between the impurity and the surrounding excitations. To this end, the impurity’s effective mass has to be...
This is a review addressing soliton-like states in systems with nonlocal nonlinearity. The work on this topic has long history in optics and related areas. Some results produced by the work (such as solitons supported by thermal nonlinearity in optic...
A new two-mode version of the generalized Zakharov-Kuznetsov equation is derived using Korsunsky’s method. This dynamical model describes the propagation of two-wave solitons moving simultaneously in the same direction with mutual interaction t...
Broken symmetries of quasi one-dimensional electronic systems give rise to microscopic solitons taking roles of carriers of the charge or spin. The double degeneracy gives rise to solitons as kinks of the scalar order parameter A; the continuous dege...
In this paper, we extend the Petviashvili method (PM) to the fractional nonlinear Schrödinger equation (fNLSE) for the construction and analysis of its soliton solutions. We also investigate the temporal dynamics and stabilities of the soliton s...
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