Electron. J. Differential Equations, Vol. 2020 (2020), No. 77, pp. 1-34.

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

Pavel I. Naumkin, Isahi Sanchez-Suarez

Abstract:
We consider the Cauchy problem for the higher-order nonlinear Schrodinger equation

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.
DOI: 10.58997/ejde.2020.77

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Pavel I. Naumkin
Centro de Ciencias Matemáticas
UNAM Campus Morelia, AP 61-3 (Xangari)
Morelia CP 58089, Michoacán, México
email: pavelni@matmor.unam.mx
  Isahi Sánchez-Suárez
Universidad Politécnica de Uruapan
CP 60210 Uruapan Michoacán, México
email: isahi_ss@hotmail.com

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