Asymptotics for the modified witham equation

Nakao Hayashi; Pavel I. Naumkin; Isahi Sánchez-Suárez

doi:10.3934/cpaa.2018069

Article Contents

2018, Volume 17, Issue 4: 1407-1448. Doi: 10.3934/cpaa.2018069

This issue Previous Article Focusing nlkg equation with singular potential Next Article Local and global existence of solutions to a strongly damped wave equation of the $ p $-Laplacian type

Asymptotics for the modified witham equation

1.
Department of Mathematics, Graduate School of Science, Osaka University, Osaka, Toyonaka 560-0043, Japan
2.
Centro de Ciencias Matemáticas, UNAM Campus Morelia, AP 61-3 (Xangari), Morelia CP 58089, Michoacán, Mexico

^* Corresponding author
^* Corresponding author

Received: July 31, 2016

Revised: April 30, 2017

Published: April 2018

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Abstract

We consider the modified Witham equation

${{\partial }_{t}}v+{{\partial }_{x}}\sqrt{{{a}^{2}}-\partial _{x}^{2}v}={{\partial }_{x}}\left( {{v}^{3}} \right),\ \ \left( t,x \right)\in \mathbb{R}\times \mathbb{R},$

where $\sqrt{a^{2}-\partial _{x}^{2}}$ means the dispersion relation which correspond to nonlinear Kelvin and continental-shelf waves. We develop the factorization technique to study the large time asymptotics of solutions.

Keywords:

Asymptotics of solutions,
modified Witham equation.

Mathematics Subject Classification: Primary: 35Q55; Secondary: 35B40.

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References

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