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March/April 2018 Asymptotics for the modified Boussinesq equation in one space dimension
Nakao Hayashi, Pavel I. Naumkin
Adv. Differential Equations 23(3/4): 239-294 (March/April 2018).

Abstract

We consider the Cauchy problem for the modified Boussinesq equation in one space dimension \begin{equation*} \begin {cases} w_{tt}=a^{2}\partial _{x}^{2}w-\partial _{x}^{4}w+\partial _{x}^{2} ( w^{3} ) ,\text{ } ( t,x ) \in \mathbb{R}^{2}, \\ w ( 0,x ) =w_{0} ( x ) ,\text{ }w_{t} ( 0,x ) =w_{1} ( x ) ,\text{ }x\in \mathbb{R}\text{,} \end {cases} \end{equation*} where $a > 0.$ We study the large time asymptotics of solutions to the Cauchy problem for the modified Boussinesq equation. We apply the factorization technique developed recently in papers [5], [6], [7], [8].

Citation

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Nakao Hayashi. Pavel I. Naumkin. "Asymptotics for the modified Boussinesq equation in one space dimension." Adv. Differential Equations 23 (3/4) 239 - 294, March/April 2018.

Information

Published: March/April 2018
First available in Project Euclid: 19 December 2017

zbMATH: 06822199
MathSciNet: MR3738647

Subjects:
Primary: 35B40, 35Q35

Rights: Copyright © 2018 Khayyam Publishing, Inc.

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Vol.23 • No. 3/4 • March/April 2018
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