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November/December 2013 Existence and Stability of a Two-Parameter Family of Solitary Waves for an NLS-KdV System
John Albert, Santosh Bhattarai
Adv. Differential Equations 18(11/12): 1129-1164 (November/December 2013).

Abstract

We prove existence and stability results for a two-parameter family of solitary-wave solutions to a system in which an equation of nonlinear Schr\"odinger type is coupled to an equation of Korteweg--de Vries type. Such systems model interactions between short and long dispersive waves. The results extend earlier results of Angulo, Albert and Angulo, and Chen. Our proof involves the characterization of solitary-wave solutions as minimizers of an energy functional subject to two constraints. To establish the precompactness of minimizing sequences via concentrated compactness, we establish the sub-additivity of the problem with respect to both constraint variables jointly.

Citation

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John Albert. Santosh Bhattarai. "Existence and Stability of a Two-Parameter Family of Solitary Waves for an NLS-KdV System." Adv. Differential Equations 18 (11/12) 1129 - 1164, November/December 2013.

Information

Published: November/December 2013
First available in Project Euclid: 4 September 2013

zbMATH: 1290.35219
MathSciNet: MR3129020

Subjects:
Primary: 35B35 , 35Q53 , 35Q55 , 5A15 , 76B25

Rights: Copyright © 2013 Khayyam Publishing, Inc.

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Vol.18 • No. 11/12 • November/December 2013
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