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首页> 外文期刊>Discrete and continuous dynamical systems >BLOW-UP SOLUTIONS FOR TWO COUPLED GROSS-PITAEVSKII EQUATIONS WITH ATTRACTIVE INTERACTIONS
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BLOW-UP SOLUTIONS FOR TWO COUPLED GROSS-PITAEVSKII EQUATIONS WITH ATTRACTIVE INTERACTIONS

机译：具有吸引力相互作用的两个耦合Pitaevskii方程的爆破解

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摘要

The paper is concerned with a system of two coupled time-independent Gross-Pitaevskii equations in R~2, which is used to model two-component Bose-Einstein condensates with both attractive intraspecies and attractive interspecies interactions. This system is essentially an eigenvalue problem of a stationary nonlinear Schrodinger system in R~2, and solutions of the problem are obtained by seeking minimizers of the associated variational functional with constrained mass (i.e. L~2—norm constaints). Under a certain type of trapping potentials V_i(x) (i = 1,2), the existence, non-existence and uniqueness of this kind of solutions are studied. Moreover, by establishing some delicate energy estimates, we show that each component of the solutions blows up at the same point (i.e., one of the global minima of V_i(x)) when the total interaction strength of intraspecies and interspecies goes to a critical value. An optimal blowing up rate for the solutions of the system is also given.
机译：本文涉及R〜2中两个时间无关的Gross-Pitaevskii方程组，该系统用于模拟具有吸引力的种内和吸引力的种间相互作用的两组分Bose-Einstein冷凝物。该系统本质上是R〜2中的平稳非线性Schrodinger系统的本征值问题，并且该问题的解决方案是通过寻找受约束质量（即L〜2范数约束）的相关变分函数的极小值来获得的。在一定类型的俘获势V_i（x）（i = 1,2）下，研究了这种解的存在性，不存在性和唯一性。此外，通过建立一些精细的能量估计，我们表明，当种内和种间的总相互作用强度达到临界值时，解决方案的每个组成部分都在同一点爆炸（即V_i（x）的全局最小值）。值。还给出了系统解决方案的最佳爆炸率。

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