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| Existence of Generalized Heteroclinic Solutions of theCoupled Schr¨odinger System under aSmall Perturbation |
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Citation： |
Shengfu DENG,Boling GUO,Tingchun WANG.Existence of Generalized Heteroclinic Solutions of theCoupled Schr¨odinger System under aSmall Perturbation[J].Chinese Annals of Mathematics B,2014,35(6):857~872 |
| Page view： 1300
Net amount： 993 |
Authors： |
Shengfu DENG; Boling GUO; Tingchun WANG; |
Foundation： |
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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| Abstract： |
The following coupled Schr\"{o}dinger system with a small perturbation
\begin{align*}
u_{xx}+u-u^3+\beta uv^2+\ep f(\ep,u, u_x,v,v_x) &=0\quad {\rm in}
\ \mathbb{R},
\v_{xx}-v+v^3+\beta u^2v+\ep g(\ep,u, u_x,v,v_x) &=0\quad {\rm in}\mathbb{R}
\end{align*}
is considered, where $\beta$ and $\ep$ 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). |
Keywords： |
Coupled Schrodinger system, Heteroclinic solutions, Reversibility |
Classification： |
34B60, 34C25, 34C37, 35B32, 37C29 |
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