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Stability of the standing waves for a class of coupled nonlinear Klein-Gordon equations

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Abstract

This paper deals with the standing waves for a class of coupled nonlinear Klein-Gordon equations with space dimension N ≥ 3, 0 < p, q < 2 / N−2 and p + q < 4/N. By using the variational calculus and scaling argument, we establish the existence of standing waves with ground state, discuss the behavior of standing waves as a function of the frequency ω and give the sufficient conditions of the stability of the standing waves with the least energy for the equations under study.

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Authors and Affiliations

  1. College of Mathematics and Software Science, Sichuan Normal University, Chengdu, 610066, China

    Jian Zhang & Zai-hui Gan

  2. Institute of Applied Physics and Computational Mathematics, Beijing, 100088, China

    Zai-hui Gan & Bo-ling Guo

Authors
  1. Jian Zhang
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  2. Zai-hui Gan
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  3. Bo-ling Guo
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Corresponding author

Correspondence to Zai-hui Gan.

Additional information

Supported by the National Natural Science Foundation of China (No. 10771151, 10801102), Sichuan Youth Sciences and Technology Foundation(No. 07ZQ026-009) and China Postdoctoral Science Foundation Funded Project.

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Zhang, J., Gan, Zh. & Guo, Bl. Stability of the standing waves for a class of coupled nonlinear Klein-Gordon equations. Acta Math. Appl. Sin. Engl. Ser. 26, 427–442 (2010). https://doi.org/10.1007/s10255-010-0008-z

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  • DOI: https://doi.org/10.1007/s10255-010-0008-z

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