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

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  • 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.

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


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