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July 2021 Large time asymptotic behavior of solutions to higher order nonlinear Schrödinger equation
Beatriz Juarez-campos, NAUMKIN Pavel I., RUIZ-PAREDES Hector F.
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Osaka J. Math. 58(3): 509-529 (July 2021).

Abstract

We consider the Cauchy problem for the higher-order nonlinear Schrödinger equation \begin{gather} \label{A} i\partial_{t}u+\frac{1}{2}\partial_{x}^{2}u-\frac{1}{4}\partial_{x}^{4} u=u^{3},\text{ }t>0,\text{ }x\in\mathbb{R}, u\left( 0,x\right) =u_{0}\left( x\right) ,\text{ }x\in\mathbb{R.} \notag \end{gather} The aim of the present paper is prove the global existence of solutions to (0.1) if the initial data $u_{0}\in\mathbf{H}^{1}\cap\mathbf{H}^{0,1}$. Also we find the large time asymptotics of solutions.

Acknowledgments

The work is partially supported by CONACYT 283698 and PAPIIT project IN100616.

Citation

Download Citation

Beatriz Juarez-campos. NAUMKIN Pavel I.. RUIZ-PAREDES Hector F.. "Large time asymptotic behavior of solutions to higher order nonlinear Schrödinger equation." Osaka J. Math. 58 (3) 509 - 529, July 2021.

Information

Received: 3 March 2020; Published: July 2021
First available in Project Euclid: 20 July 2021

Subjects:
Primary: 35B40, 35Q35

Rights: Copyright © 2021 Osaka University and Osaka City University, Departments of Mathematics

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Vol.58 • No. 3 • July 2021
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