A proof of existence of stationary dark soliton solutions of the cubic-quintic nonlinear Schrödinger equation with a periodic potential is given. It is based on the interpretation of the dark soliton as a heteroclinic on the Poincaré map.

We study the issue of stability of static soliton-like solutions in some non-linear field theories which allow for knotted field configurations. Concretely, we investigate the AFZ model, based on a La-grangian quartic in first derivatives with infinitely many conserved currents, for which infinitely many soliton solutions are known analytically. For this model we find that sectors with differen...

The 2-soliton solutions of the Korteweg-de Vries equation satisfy a fourth-order nonlinear ordinary differential equation which depends on two parameters λ, μ. As is well known, for each fixed choice of (λ, μ) in R, the ODE is actually a completely integrable Hamiltonian system with two degrees of freedom. Here we address the question of whether the soliton and 2-soliton solutions of KdV are th...

We study a general class of line-soliton solutions of the Kadomtsev-Petviashvili II KPII equation by investigating the Wronskian form of its tau-function. We show that, in addition to the previously known line soliton solutions of KPII, this class also contains a large variety of multisoliton solutions, many of which exhibit nontrivial spatial interaction patterns. We also show that, in general...

In this paper, a (2+1)-dimensional Caudrey–Dodd–Gibbon–Kotera–Sawada system is investigated in fluid mechanics via the symbolic computation. With help of Hirota method, we derive some singular soliton, shock-wave, breather-stripe soliton and hybrid solutions. Based on finite difference get numerical one-soliton We graphically show shock-wave solutions, observe that solutions are explosive unsta...

The nonlinear Schrödinger equation (NLSE) is a central model of nonlinear science, applying to hydrodynamics, plasma physics, molecular biology and optics. The NLSE admits only few elementary analytic solutions, but one in particular describing a localized soliton on a finite background is of intense current interest in the context of understanding the physics of extreme waves. However, althoug...

Binary Bargmann symmetry constraints are applied to decompose soliton equations into finite-dimensional Liouville integrable Hamiltonian systems, generated from so-called constrained flows. The resulting constraints on the potentials of soliton equations give rise to involutive solutions to soliton equations, and thus the integrability by quadratures are shown for soliton equations by the const...