The Darboux transformation (DT) for the coupled complex short pulse (CCSP) equation is constructed through loop group method. DT then utilized to construct various exact solutions including bright soliton, dark-soliton, breather and rogue wave CCSP equation. In case of vanishing boundary condition (VBC), we perform inverse scattering analysis understand soliton solution better. Breather are in ...

A self-adaptive mesh method is proposed for the numerical simulations of the Camassa-Holm equation based on its integrable semi-discretization. It is an integrable scheme, possessing the N-soliton solution (see J. Phys. A, 41 355205). Moreover, it is called a self-adaptive mesh method, because the non-uniform mesh is driven and adapted automatically by the solution. Once the non-uniform mesh is...

: optical separate spatial dark and bright soliton pairs in steady-state case in one dimension, for a series circuit consisting of two-photon photorefractive (pr) crystal are investigated. each crystal can be supported the spatial soliton, and at least one must be photovoltaic. the two solitons are known collectively as separate spatial soliton pairs with dark–dark, bright–dark and bright–brigh...

Multisoliton solutions are derived for a general nonlinear Schrödinger equation with derivative by using Hirota's approach. The dynamics of one-soliton solution and two-soliton interactions are also illustrated. The considered equation can reduce to nonlinear Schrödinger equation with derivative as well as the solutions.

We introduce and study a new type of soliton with potential Reeb vector field on Riemannian manifolds an almost paracontact structure corresponding to paracomplex structure. The special cases para-Einstein-like, para-Sasaki-like having torse-forming were considered. It was proved necessary sufficient condition for the manifold admit para-Ricci-like soliton, which is that para-Einstein-like. Exp...

We derive a bound on the energy of the general (p,q)-supersymmetric two-dimensional massive sigma model with torsion, in terms of the topological and Noether charges that appear as central charges in its supersymmetry algebra. The bound is saturated by soliton solutions of first-order Bogomol'nyi-type equations. This generalizes results obtained previously for p = q models without torsion. We g...