Multisoliton Solutions and Breathers for the Coupled Nonlinear Schrödinger Equations via the Hirota Method

Abstract

Under investigation in this paper are the coupled nonlinear Schrödinger (CNLS) equations with dissipation terms by the Hirota method, which are better than the formal Schrödinger equation in eliciting optical solitons. The bilinear form has been constructed, via which multisolitons and breathers are derived. In particular, the three-bright soliton solution and breathers are derived and simulated via some pictures. The propagation characters are analysed with the change of the parameters.

High-order rational solutions and rogue wave for the (2 + 1)-dimensional nonlinear Schrödinger equation

“…Hence finding the RW of NLS equation is a topic of great significance. In the last decades, a variety of construction methods for RW solution of NLS equation have been established, such as the Hirota's bilinear method [21][22][23], the Darboux transformation method [24], the inverse scattering method [25]. Generally, it is easy to derive the RWs of (1+1)-dimensional NLS equations, but the higher-dimensional ones are not simple.…”

New Exact Solutions for the Coupled Nonlinear Schrödinger Equations with Variable Coefficients

“…Many researchers have studied the CNLS equation with constant coefficient. In recent years, a number of methods are used to solve the coupled integrable nonlinear models, such as Hirota bilinear method [1] [2] [3], Painlev analysis method [4], Function expansion method [5] and direct perturbation method [6] and so on. However, the evolutions of vector solitons for CNLS equation with constant coefficients are not dependent on any controllable parameters.…”