KdV type asymptotics for solutions to higher-order nonlinear Schrodinger equations

Abstract

We consider the Cauchy problem for the higher-order nonlinear Schrodinger equation $$\displaylines{ i\partial_t u-\frac{a}{3}| \partial_x| ^3u-\frac{b}{4}\partial_x^4u =\lambda i\partial_x(| u|^2u),\quad (t,x) \in\mathbb{R}^{+}\times \mathbb{R},\cr u(0,x) =u_0(x),\quad x\in\mathbb{R}, }$$ where \(a,b>0\), \(| \partial_x| ^{\alpha}=\mathcal{F}^{-1}| \xi| ^{\alpha}\mathcal{F}\) and \(\mathcal{F}\) is the Fourier transformation. Our purpose is to study the large time behavior of the solutions under the non-zero mass condition \(\int u_0(x)\,dx\neq 0\).
 For more information see https://ejde.math.txstate.edu/Volumes/2020/77/abstr.html