Related papers: KdV soliton interactions: a tropical view
The Korteweg-de Vries (KdV) equation governs the propagation of nonlinear internal and surface gravity waves in shallow ocean environments, where the balance between nonlinear steepening and frequency-dependent dispersion produces solitons.…
We consider the vector generalization of the modified Korteweg-de Vries equation. We develop the inverse scattering transform for solving this equation. We construct the solitons and the breather solutions and investigate the processes of…
The aim of this work is to study solitary water wave interactions between two topographic obstacles for the forced Korteweg-de Vries equation (fKdV). Focusing on the details of the interactions, we identify regimes in which solitary wave…
We study the stability and dynamics of solitons in the Korteweg-de Vries (KdV) equation in the presence of noise and deterministic forcing. The noise is space-dependent and statistically translation-invariant. We show that, for small…
By introducing in the hydrodynamic model, i.e. in the hydrodynamic equations and the corresponding boundary conditions, the higher order terms in the deviation of the shape, we obtain in the second order the Korteweg de Vries equation…
We study a particular deformation of the potential KdV model (pKdV) and construct the quasi-conservation laws by a direct method. The charge densities, differing from their integrable counterpart with homogeneous degree terms, exhibit mixed…
For the focusing energy critical wave equation in 5D, we construct a solution showing the inelastic nature of the collision of any two solitons, except the special case of two solitons of same scaling and opposite signs. Beyond its own…
Nonlinear non-Abelian Korteweg-de Vries (KdV) and modified Korteweg-de Vries (mKdV) equations and their links via Baecklund transformations are considered. The focus is on the construction of soliton solutions admitted by matrix modified…
A new model for Korteweg and de-Vries equation (KdV) is derived. The system under study is an open channel consisting of two concentric cylinders, rotating about their vertical axis, which is tilted by slope {\tau} from the inertial…
The light-cone gauge approach to $T\overline{T}$ deformed models is used to derive the $T\overline{T}$ deformed matrix nonlinear Schr\"odinger equation, the Landau--Lifshitz equation, and the Gardner equation. Properties of one-soliton…
We study the behavior of the soliton which, while moving in non-dissipative medium encounters a barrier with dissipation. The modelling included the case of a finite dissipative layer as well as a wave passing from a dissipative layer into…
This letter introduces the novel concept of Painlev\'e solitons -- waves arising from the interaction between Painlev\'e waves and solitons in integrable systems. Painlev\'e solitons may also be viewed as solitons propagating against a…
We consider the problem of quantization of classical soliton integrable systems, such as the KdV hierarchy, in the framework of a general formalism of Gaudin models associated to affine Kac--Moody algebras. Our experience with the Gaudin…
We report results of systematic numerical analysis of collisions between two and three stable dissipative solitons in the two-dimensional (2D) complex Ginzburg- Landau equation (CGLE) with the cubic-quintic (CQ) combination of gain and loss…
By means of analytical and numerical methods, we study how the residual three-dimensionality affects dynamics of solitons in an attractive Bose-Einstein condensate loaded into a cigar-shaped trap. Based on an effective 1D Gross-Pitaevskii…
The propagation of localized solitons in the presence of large-scale waves is a fundamental problem, both physically and mathematically, with applications in fluid dynamics, nonlinear optics and condensed matter physics. Here, the evolution…
Hirota's discrete Korteweg-de Vries equation (dKdV) is an integrable partial difference equation on 2-dimensional integer lattice, which approaches the Korteweg-de Vries equation in a continuum limit. We find new transformations to other…
For the KdV equation with box type initial data, the interaction between a trial soliton and large-scale dispersive mean flow is studied theoretically and numerically. The pure box initial value can cause rarefaction wave and dispersive…
We construct a definition of the weak solution to KdV type equations with small dispersion admitting the zero dispersion limit for soliton-like solutions. Using this definition, we obtain a system of equations (the limit problem as the…
The results of recent experiments [1] on observing soliton lattices and their dislocations in vertical cylindrical channels filled with immiscible fluids with strongly different viscosities and but slightly different densities are…