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

Date

2020-07-22

Authors

Naumkin, Pavel I.
Sanchez-Suarez, Isahi

Journal Title

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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. <i>Electronic Journal of Differential Equations, 2020</i>(77), pp. 1-34.

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Attribution 4.0 International

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This work is licensed under a Creative Commons Attribution 4.0 International License.

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