Related papers: Mach-Type Soliton in the Novikov-Veselov Equation
Using the reality condition of the solutions, one constructs the real Pfaffian N-solitons solutions of the Novikov-Veselov (NV) equation using the $\tan$ function and the Schur identity. By the minor-summation formula of the Pfaffian, we…
We construct the $N$-solitons solution in the Novikov-Veselov equation from the extended Moutard transformation and the Pfaffian structure. Also, the corresponding wave functions are obtained explicitly. As a result, the property…
We consider KdV-type equations with $C^1$ nonhomogeneous nonlinearities and small dispersion $\varepsilon$. The first result consists in the conclusion that, in the leading term with respect to $\varepsilon$, the solitary waves in this…
We consider the initial value problems of the Kadomtsev-Petviashvili (KP) equation for symmetric V-shape initial waves consisting of two semi-infinite line solitons with the same amplitude. Numerical simulations show that the solutions of…
The dynamics of initially truncated and bent line solitons for the Kadomtsev-Petviashvili (KPII) equation modelling internal and surface gravity waves are analysed using modulation theory. In contrast to previous studies on obliquely…
The main purpose of the paper is to provide a survey of our recent studies on soliton solutions of the Kadomtsev-Petviashvili (KP) equation. The classification is based on the far-field patterns of the solutions which consist of a finite…
We study the spectral stability of smooth, small-amplitude periodic traveling wave solutions of the Novikov equation, which is a Camassa-Holm type equation with cubic nonlinearities. Specifically, we investigate the…
We report results of systematic numerical studies of 2D matter-wave soliton families supported by an external potential, in a vicinity of the junction between stable and unstable branches of the families, where the norm of the solution…
Resonant Y-shaped soliton solutions to the Kadomtsev-Petviashvili II (KPII) equation are modelled as shock solutions to an infinite family of modulation conservation laws. The fully two-dimensional soliton modulation equations, valid in the…
This gives a survey of our recent studies on soliton solutions of the Kadomtsev-Petviashvili equation with an emphasis on the Mach reflection problem in shallow water.
The oblique collisions and dynamical interference patterns of two-dimensional dispersive shock waves are studied numerically and analytically via the temporal dynamics induced by wedge-shaped initial conditions for the…
We study numerically the evolution of perturbed Korteweg-de Vries solitons and of well localized initial data by the Novikov-Veselov (NV) equation at different levels of the "energy" parameter $ E $. We show that as $ |E| \to \infty $, NV…
Using numerical modeling investigated interaction of solitary waves (solitons) of the regularized long wave equation. For reception the stable model of the nonlinear medium are used methods of the linear prediction and progressive…
Nonlinear solitary solutions to the Vlasov-Poisson set of equations are studied in order to investigate their stability by employing a fully-kinetic simulation approach. The study is carried out in the ion-acoustic regime for a…
The aim of this article is to explain why similar weak stability criteria appear in both the construction of steady Mach stem configurations bifurcating from a reference planar shock wave solution to the compressible Euler equations, as…
In this paper we study the Nonlinear Schr\"odinger-Maxwell equations (NSM). We are interested to analyse the existence of solitons, namely of finite energy solutions which exhibit stability properties. This paper is divided in two parts. In…
We consider the linear stability of chiral matter-wave solitons described by a density-dependent gauge theory. By studying the associated Bogoliubov-de Gennes equations both numerically and analytically, we find that the stability problem…
It is studied the scattering of magnons by the 2d topological Belavin-Polyakov soliton in isotropic ferromagnet. Analytical solutions of the scattering problem are constructed: (i) exactly for any magnon wave vectors for the partial wave…
The Kadomtsev-Petviashvili (KP) equation describes weakly dispersive and small amplitude waves propagating in a quasi-two dimensional situation. Recently a large variety of exact soliton solutions of the KP equation has been found and…
We introduce a general model which augments the one-dimensional nonlinear Schr\"{o}dinger (NLS) equation by nonlinear-diffraction terms competing with the linear diffraction. The new terms contain two irreducible parameters and admit a…