相关论文: Soliton Resonances for MKP-II

We consider $N$-soliton solutions of the KP equation, (-4u_t+u_{xxx}+6uu_x)_x+3u_{yy}=0 . An $N$-soliton solution is a solution $u(x,y,t)$ which has the same set of $N$ line soliton solutions in both asymptotics $y\to\infty$ and $y\to…

Soliton solutions of the KP equation have been studied since 1970, when Kadomtsev and Petviashvili proposed a two-dimensional dispersive wave equation now known as the KP equation. It is well-known that one can use the Wronskian method to…

A moving frame formulation of geometric non-stretching flows of curves in the Riemannian symmetric spaces $Sp(n+1)/Sp(1)\times Sp(n)$ and $SU(2n)/Sp(n)$ is used to derive two bi-Hamiltonian hierarchies of symplectically-invariant soliton…

Some soliton equation in 2+1 dimensions and their 1+1 and/or dimensional integrable reductions are considered.

We study the maximum wave amplitude produced by line-soliton interactions of the Kadomtsev-Petviashvili II (KPII) equation, and we discuss a mechanism of generation of large amplitude shallow water waves by multi-soliton interactions of…

A double-layer Kerr resonator in which both coupled modes are excited and interact with each other via incoherent cross-phase modulation is investigated to reveal stable localized solutions beyond the usual formation mechanism involving a…

This article offers a review of results for solitons in 2D and 3D models of nonlinear dissipative media. The existence of such solitons requires to maintain two balances: between nonlinear self-focusing and linear diffraction and/or…

Bending of solitons in two dimensional plane is presented in the presence of weak and slowly varying inhomogeneous ion density for the propagation of ion acoustic soliton in unmagnetized cold plasma with isothermal electrons. Using…

In this article we study the generalized dispersion version of the Kadomtsev-Petviashvili II equation, on $\T \times \R$ and $\T \times \R^2$. We start by proving bilinear Strichartz type estimates, dependent only on the dimension of the…

Due to higher-order Kaup-Newell (KN) system has more complex and diverse solutions than classical second-order flow KN system, the research on it has attracted more and more attention. In this paper, we consider a higher-order KN equation…

We study rational solutions of the Boussinesq equation, which is a soliton equation solvable by the inverse scattering method. These rational solutions, which are algebraically decaying and depend on two arbitrary parameters, are expressed…

We present a first-principles derivation of the variational equations describing the dynamics of the interaction of a spatial soliton and a surface plasmon polariton (SPP) propagating along a metal/dielectric interface. The variational…

The N=2 supersymmetric KdV equations are studied within the framework of Hirota's bilinear method. For two such equations, namely $N=2, a=4$ and $N=2, a=1$ supersymmetric KdV equations, we obtain the corresponding bilinear formulations.…

We consider the soliton solutions of a recently proposed coupled Sasa-Satsuma-mKdV equation using the Kadomtsev-Petviashvili reduction method. The system consists of a complex-valued component coupled with a real-valued one. Under zero or…

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 introduce an extension of the \ell-reduced KP hierarchy, which we call the \ell-Bogoyavlensky hierarchy. Bogoyavlensky's 2+1-dimensional extension of the KdV equation is the lowest equation of the hierarchy in case of \ell=2. We present…

In this work, we present a general procedure, which is able to generate new exact solitonic models in 1+1 dimensions, from a known one, consisting of two coupled scalar fields. An interesting consequence of the method, is that of the…

We study two dimensional soliton solutions in the $CP^2$ nonlinear $\sigma$-model with a Dzyaloshinskii-Moriya type interaction. First, we derive such a model as a continuous limit of the $SU(3)$ tilted ferromagnetic Heisenberg model on a…

We propose compact finite difference schemes to solve the KP equations $u\_t + u\_{xxx} + u^p u\_x + $\lambda$ \partial^{--1}\_x u\_{yy} = 0$. When $p = 1$, this equation describes the propagation of small amplitude long waves in shallow…

The Kadomtsev--Petviashvili (KP) hierarchy is the archetype of infinite-dimensional integrable systems, which describes nonlinear ion acoustic waves in two-dimensional space. This remarkably ordered system resides on a singular submanifold…