Well-Posedness for Multicomponent Schrödinger–gKdV Systems and Stability of Solitary Waves with Prescribed Mass
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In this paper we prove the well-posedness issues of the associated initial value problem, the existence of nontrivial solutions with prescribed \(L^2\)-norm, and the stability of associated solitary waves for two classes of coupled nonlinear dispersive equations. The first problem here describes the nonlinear interaction between two Schrödinger type short waves and a generalized Korteweg-de Vries type long wave and the second problem describes the nonlinear interaction of two generalized Korteweg-de Vries type long waves with a common Schrödinger type short wave. The results here extend many of the previously obtained results for two-component coupled Schrödinger–Korteweg-de Vries systems.
KeywordsSchrödinger–KdV equations Local and global well-posedness Smoothing effects Bourgain space Normalized solutions Solitary waves Stability Variational methods
Mathematics Subject Classification35Q53 35Q55 35B35 35B65 35A15
The authors are thankful to Professor John Albert and Professor Felipe Linares for their teaching. A. J. Corcho was partially supported by CAPES and CNPq/Edital Universal - 481715/2012-6, Brazil and M. Panthee acknowledges supports from Brazilian agencies: FAPESP 2016/25864-6 and CNPq 305483/2014-5.
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