Stable solitary-waves in a higher order generalized nonlinear Schrödinger equation with space- and time-variable coefficients

Abstract

We developed a method that combines a similarity transformation with a mapping that solves a generalized nonautonomous nonlinear Schrödinger (NLS) equation containing cubic, quintic and higher order terms in the conjunction with spatially and temporary varying dispersion, containing higher nonlinearities, and external potential. We have studied various classes of solutions in closed form representing front, bright and dark solitary-like waves. We introduced a transformation that solves the related transformed NLS in the constant coefficients. As an application of this technique, we have analyzed the dynamical behavior of several specific classes of solutions such as moving, breathing, resonant both for periodic and quasi-periodic solitary-like waves. The stability of the obtained solitary-like waves is examined using analytical and numerical methods.