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On soliton solutions to a class of Schrödinger-K $ \mathbf{d}$V systems


Authors: Chungen Liu and Youquan Zheng
Journal: Proc. Amer. Math. Soc. 141 (2013), 3477-3484
MSC (2010): Primary 35J10, 35J50, 35J60
Published electronically: June 12, 2013
MathSciNet review: 3080170
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Abstract: In this paper, we consider a class of coupled nonlinear Schrödinger-KdV systems in the whole space via the Nehari manifold method. The existence of nontrivial solutions with both of the components nonzero is obtained.


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Additional Information

Chungen Liu
Affiliation: School of Mathematical Sciences and LPMC, Nankai University, Tianjin 300071, People’s Republic of China
Email: liucg@nankai.edu.cn

Youquan Zheng
Affiliation: School of Mathematical Sciences, Nankai University, Tianjin 300071, People’s Republic of China
Email: zhengyq@mail.nankai.edu.cn

DOI: https://doi.org/10.1090/S0002-9939-2013-11629-1
Keywords: Schr\"odinger-KdV systems, Nehari manifold, nontrivial solution
Received by editor(s): March 30, 2011
Received by editor(s) in revised form: December 11, 2011
Published electronically: June 12, 2013
Additional Notes: The first author was partially supported by NFSC (11071127, 10621101), the 973 Program of STM of China (2011CB808002) and SRFDP
Communicated by: Yingfei Yi
Article copyright: © Copyright 2013 American Mathematical Society