Related papers: Modulation theory for soliton resonance and Mach r…
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…
The Kadomtsev-Petviashvili II (KPII) equation admits a large variety of multi-soliton solutions which exhibit both elastic as well as inelastic types of interactions. This work investigates a general class of multi-solitons which were not…
We consider perturbations of the non-unitary minimal model solutions of two-dimensional conformal turbulence proposed by Polyakov. Demanding the absence of non-integrable singularities in the resulting theories leads to constraints on the…
An overview of the inverse scattering theory of the Kadomtsev Petviashvili II equation with an emphasis on the inverse problem for perturbed KP multi line solitons is provided. It is shown that, despite additional algebraic or analytic…
The nature of the magnetic structure arising from ion specular reflection in shock compression studies is examined by means of 1d particle in cell simulations. Propagation speed, field profiles and supporting currents for this magnetic…
The Direct and the Inverse Scattering Problems for the heat operator with a potential being a perturbation of an arbitrary $N$ soliton potential are formulated. We introduce Jost solutions and spectral data and present their properties.…
The novel generalized perturbation (n, M)-fold Darboux transformations (DTs) are reported for the (2+1)-dimensional Kadomtsev-Petviashvili (KP) equation and its extension by using the Taylor expansion of the Darboux matrix. The generalized…
Here, a novel 2+1-dimensional nonlinear evolution equation with temporal modulation is introduced which admits integrable Ermakov-Painlev\'e II symmetry reduction. Application is made to obtain exact solution to a class of Stefan-type…
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…
The small oscillations of solitons in 2D Bose-Einstein condensates are investigated by solving the Kadomtsev-Petviashvili equation which is valid when the velocity of the soliton approaches the speed of sound. We show that the soliton is…
Whitham modulation theory describes the zero dispersion limit of nonlinear waves by a system of conservation laws for the parameters of modulated periodic traveling waves. Here, admissible, discontinuous, weak solutions of the Whitham…
We derive the modulation equations or Whitham equations for the Camassa--Holm (CH) equation. We show that the modulation equations are hyperbolic and admit bi-Hamiltonian structure. Furthermore they are connected by a reciprocal…
Some models providing shell-shaped static solutions with compact support (compactons) in 3+1 and 4+1 dimensions are introduced, and the corresponding exact solutions are calculated analytically. These solutions turn out to be topological…
We introduce a dynamical model of a Bose-Einstein condensate based on the 2D Gross-Pitaevskii equation, in which the nonlinear coefficient is a function of radius. The model describes a situation with spatial modulation of the negative…
We study the dynamics of solitons as solutions to the perturbed KdV (pKdV) equation $\partial_t u = -\partial_x (\partial_x^2 u + 3u^2-bu)$, where $b(x,t) = b_0(hx,ht)$, $h\ll 1$ is a slowly varying, but not small, potential. We option an…
A general form of $N$-dark soliton solutions of the multi-component Mel'nikov system is presented. Taking the coupled Mel'nikov system comprised of two-component short waves and one-component long wave as an example, its general…
A functional of the solution of the Kadomtsev-Petviashvili II equation maps multi-soliton solutions onto systems of vertices - structures that are localized around soliton junctions. A solution with one junction is mapped onto a single…
The Kadomtsev-Petviashvili (KP) equation possesses a four-parameter family of one-dimensional periodic traveling waves. We study the spectral stability of the waves with small amplitude with respect to two-dimensional perturbations which…
We consider a simple model system supporting stable solitons in two dimensions. The system is the parametrically driven damped nonlinear Schr\"odinger equation, and the soliton stabilises for sufficiently strong damping. The purpose of this…
Using the reality condition of the solutions, one constructs the Mach-type soliton of the Novikov-Veselov equation by the minor-summation formula of the Pfaffian. We study the evolution of the Mach-type soliton and find that the amplitude…