Related papers: Interaction properties of complex mKdV solitons
The existence, stability and other dynamical properties of a new type of multi-dimensional (2D or 3D) solitons supported by a transverse low-dimensional (1D or 2D, respectively) periodic potential in the nonlinear Schr\"{o}dinger equation…
This study aims to investigate the interactions of solitons with an external force within the framework of the Schamel equation, both asymptotically and numerically. By utilizing asymptotic expansions, we demonstrate that the soliton…
A new kinematic condition for soliton motions of an $n$-dimensional continuum in $R^{n+m}$, independent of the underlying physics, is proven. The condition and its consequences for different cases are demonstrated. A soliton in a 1D string…
The dynamics of two-component solitons with a small spatial displacement of the high-frequency (HF) component relative to the low-frequency (LF) one is investigated in the framework of the Zakharov-type system. In this system, the evolution…
We derive a (2+1)-dimensional multicomponent long-wave$-$short-wave resonance interaction (LSRI) system as the evolution equation for propagation of $N$-dispersive waves in weak Kerr type nonlinear medium in the small amplitude limit. The…
Mean-field dynamics of strongly interacting bosons described by hard core bosons with nearest-neighbor attraction has been shown to support two species of solitons: one of Gross-Pitaevskii (GP-type) where the condensate fraction remains…
A multidimensionally consistent generalisation of Hirota's discrete KdV equation is proposed, it is a quad equation defined by a polynomial that is quadratic in each variable. Soliton solutions and interpretation of the model as…
Solitons in liquid crystals are spatially localised stable configuration of the liquid crystal orientational order parameter that exhibit emergent particle-like properties such as mutual interaction, translational motion and reconfigurable…
The stability and collapse of fundamental unstaggered bright solitons in the discrete Schrodinger equation with the nonpolynomial on-site nonlinearity, which models a nearly one-dimensional Bose-Einstein condensate trapped in a deep optical…
Soliton molecules have been experimentally discovered in optics and theoretically investigated for coupled systems. This paper is concerned with the formation of soliton molecules by the resonant mechanism for a noncoupled system, the…
Quantum and classical integrable systems share common mathematical structures, and the phenomena appearing in them are interrelated. Solitons, which universally appear in classical integrable systems, also appear in quantum integrable…
We study the problem of 2-soliton collision for the generalized Korteweg-de Vries equations, completing some recent works of Y. Martel and F. Merle. We classify the nonlinearities for which collisions are elastic or inelastic. Our main…
A study of high-order solitons in three nonlocal nonlinear Schr\"{o}dinger equations is presented, which includes the \PT-symmetric, reverse-time, and reverse-space-time nonlocal nonlinear Schr\"{o}dinger equations. General high-order…
An analog of the lattice KdV equation of Nijhoff et al. is constructed on a hexagonal lattice. The resulting system of difference equations exhibits soliton solutions with interesting local structure: there is a nontrivial phase shift on…
Under the effect of common perturbations, the multiple-soliton solution of the KdV equation is transformed into a sum of an elastic and a first-order inelastic component. The elastic component is a perturbation series, identical in…
Nonlinear effects in the propagation of perturbations in a dusty electron-ion plasma is studied, considering fully relativistic wave motion. A multifluid model is considered for the particles, from which a KdV equation can be derived. In…
The existence of bright solitons in the model of the Tonks-Girardeau (TG) gas with dipole-dipole (DD) interactions is reported. The governing equation is taken as the quintic nonlinear Schr\"{o}dinger equation (NLSE) with the nonlocal cubic…
We discuss the characteristic properties of noncommutative solitons moving with constant velocity. As noncommutativity breaks the Lorentz symmetry, the shape of moving solitons is affected not just by the Lorentz contraction along the…
We produce soliton and similarity solutions of supersymmetric extensions of Burgers, Korteweg-de Vries and modified KdV equations. We give new representations of the $\tau$-functions in Hirota bilinear formalism. Chiral superfields are used…
By methods of numerical simulations the dynamics of interaction of radially symmetric Bellavin-Polyakov type topological vortex in (2+1)-dimensional O(3) nonlinear sigma model is investigated. Obtained numerically the model of topological…