Inverse scattering transform and multi-solition solutions for the sextic
nonlinear Schrödinger equation
Abstract
In this work, we consider the inverse scattering transform and
multi-solition solutions of the sextic nonlinear
Schr\“{o}dinger equation. The Jost functions of
spectrum problem are derived directly, and the scattering data with
$t=0$ are obtained according to analyze the symmetry and other related
properties of the Jost functions. Then we take use of translation
transformation to get the relation between potential and kernel, and
recover potential according to Gel’fand-Levitan-Marchenko (GLM) integral
equations. Furthermore, the time evolution of scattering data is
considered, on the basic of that, the multi-solition solutions are
derived. In addition, some solutions of the equation are analyzed and
revealed its dynamic behavior via graphical analysis, which could be
enriched the nonlinear phenomena of the sextic nonlinear
Schr\”{o}dinger equation.