Integrability of the coupled cubic–quintic complex Ginzburg–Landau equations and multiple-soliton solutions via mathematical methods

Abstract

This paper is devoted to study the (1+1)-dimensional coupled cubic–quintic complex Ginzburg–Landau equations (cc–qcGLEs) with complex coefficients. This equation can be used to describe the nonlinear evolution of slowly varying envelopes of periodic spatial–temporal patterns in a convective binary fluid. Dispersion relation and properties of cc–qcGLEs are constructed. Painlevé analysis is used to check the integrability of cc–qcGLEs and to establish the Bäcklund transformation form. New traveling wave solutions and a general form of multiple-soliton solutions of cc–qcGLEs are obtained via the Bäcklund transformation and simplest equation method with Bernoulli, Riccati and Burgers’ equations as simplest equations.