EXISTENCE AND STABILITY OF STANDING WAVES FOR A COUPLED NONLINEAR SCHRDINGER SYSTEM |
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引用本文: | 曾小雨,张贻民,周焕松.EXISTENCE AND STABILITY OF STANDING WAVES FOR A COUPLED NONLINEAR SCHRDINGER SYSTEM[J].数学物理学报(B辑英文版),2015(1):45-70. |
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作者姓名: | 曾小雨 张贻民 周焕松 |
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作者单位: | Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences |
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基金项目: | supported by NSFC(11471331,11101418 and 11271360) |
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摘 要: | We study the existence and stability of the standing waves of two coupled Schrdinger equations with potentials |x|bi(bi ∈ R, i = 1, 2). Under suitable conditions on the growth of the nonlinear terms, we first establish the existence of standing waves of the Schrdinger system by solving a L2-normalized minimization problem, then prove that the set of all minimizers of this minimization problem is stable. Finally, we obtain the least energy solutions by the Nehari method and prove that the orbit sets of these least energy solutions are unstable, which generalizes the results of 11] where b1= b2= 2.
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关 键 词: | nonlinear Schrdinger system constrained variational problem standing waves orbital stubility |
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