KdV type asymptotics for solutions to higher-order nonlinear Schrödinger equations
Date
2020-07-22
Authors
Naumkin, Pavel I.
Sanchez-Suarez, Isahi
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
We consider the Cauchy problem for the higher-order nonlinear Schrödinger equation
i∂tu - α/3 |∂x|3u - b/4 ∂4xu = λi∂x(|u|2u), (t, x) ∈ ℝ⁺ x ℝ,
u(0, x) = u0(x), x ∈ ℝ,
where α, b > 0, |∂x|α = F-1|ξ|α F and F is the Fourier transformation. Our purpose is to study the large time behavior of the solutions under the non-zero mass condition ∫ u0(x)dx ≠ 0.
Description
Keywords
Nonlinear Schrödinger equation, Large time asymptotic behavior, Critical nonlinearity, Self-similar solutions
Citation
Naumkin, P. I., & Sánchez-Suárez, I. (2020). KdV type asymptotics for solutions to higher-order nonlinear Schrödinger equations. Electronic Journal of Differential Equations, 2020(77), pp. 1-34.
Rights
Attribution 4.0 International
Rights Holder
This work is licensed under a Creative Commons Attribution 4.0 International License.