Electronic Journal of Differential Equations, 
Vol. 2020 (2020), No. 77, pp. 1-34.

Title: KdV type asymptotics for solutions to higher-order nonlinear Schrodinger equations
       
Authors: Pavel I. Naumkin (UNAM Campus Morelia, Michoacan, Mexico)
         Isahi Sanchez-Suarez (Univ. Politecnica de Uruapan, Michoacan, Mexico)

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 $\int u_0(x)\,dx\neq 0$.
 
Submitted June 2, 2018. Published July 22, 2020.
Math Subject Classifications: 35B40, 35Q35.
Key Words: Nonlinear Schrodinger equation; large time asymptotic behavior;
           critical nonlinearity; self-similar solutions.