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Existence of generalized heteroclinic solutions of the coupled Schrödinger system under a small perturbation

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Abstract

The following coupled Schrödinger system with a small perturbation

$$\begin{array}{*{20}c} {u_{xx} + u - u^3 + \beta uv^2 + \varepsilon f(\varepsilon ,u,u_x ,v,v_x ) = 0 in \mathbb{R},} \\ {v_{xx} - v + v^3 + \beta u^2 v + \varepsilon g(\varepsilon ,u,u_x ,v,v_x ) = 0 in \mathbb{R}} \\ \end{array}$$

is considered, where β and ∈ are small parameters. The whole system has a periodic solution with the aid of a Fourier series expansion technique, and its dominant system has a heteroclinic solution. Then adjusting some appropriate constants and applying the fixed point theorem and the perturbation method yield that this heteroclinic solution deforms to a heteroclinic solution exponentially approaching the obtained periodic solution (called the generalized heteroclinic solution thereafter).

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Author information

Authors and Affiliations

  1. Department of Mathematics, Zhanjiang Normal University, Zhanjiang, Guangdong, 524048, China

    Shengfu Deng

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

    Boling Guo

  3. School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing, 210044, China

    Tingchun Wang

Authors
  1. Shengfu Deng
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  2. Boling Guo
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  3. Tingchun Wang
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Corresponding author

Correspondence to Tingchun Wang.

Additional information

This work was supported by the National Natural Science Foundation of China (Nos. 11126292, 11201239, 11371314), the Guangdong Natural Science Foundation (No. S2013010015957) and the Project of Department of Education of Guangdong Province (No. 2012KJCX0074).

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Deng, S., Guo, B. & Wang, T. Existence of generalized heteroclinic solutions of the coupled Schrödinger system under a small perturbation. Chin. Ann. Math. Ser. B 35, 857–872 (2014). https://doi.org/10.1007/s11401-014-0867-3

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  • DOI: https://doi.org/10.1007/s11401-014-0867-3

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