On the Cauchy problem for the Zakharov-Rubenchik/ Benney-Roskes system

Hung Luong; Norbert J. Mauser; Jean-Claude Saut

doi:10.3934/cpaa.2018075

Article Contents

2018, Volume 17, Issue 4: 1573-1594. Doi: 10.3934/cpaa.2018075

This issue Previous Article On special regularity properties of solutions of the Zakharov-Kuznetsov equation Next Article Modified scattering for the Klein-Gordon equation with the critical nonlinearity in three dimensions

On the Cauchy problem for the Zakharov-Rubenchik/ Benney-Roskes system

1.
Fak. Mathematik, University of Vienna, Oskar MorgensternPlatz 1, A-1090 Wien, Austria
2.
Wolfgang Pauli Institute c/o Fak. Math. Univ. Vienna, Oskar MorgensternPlatz 1, A-1090 Wien, Austria
3.
Laboratoire de Mathématiques, UMR 8628, Université Paris-Saclay, Paris-Sud and CNRS, F-91405 Orsay, France

Received: March 2017

Revised: February 2018

Published: April 2018

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Abstract

We address various issues concerning the Cauchy problem for the Zakharov-Rubenchik system(known as the Benney-Roskes system in water waves theory), which models the interaction of short and long waves in many physical situations. Motivated by the transverse stability/instability of the one-dimensional solitary wave (line solitary), we study the Cauchy problem in the background of a line solitary wave.

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Mathematics Subject Classification: Primary: 35Q35; Secondary: 35Q55.

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