Global Behavior of Solutions to Generalized Gross-Pitaevskii Equation
Global Behavior of Solutions to Generalized Gross-Pitaevskii Equation
复制标题
广义 Gros-Pitaevskii 方程解的全局行为
DOI：
10.1007/s12591-022-00609-8
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发表时间：
2022
影响因子：
1
通讯作者：
Miyazaki Hayato
中科院分区：
文献类型：
--
作者：
Masaki Satoshi;Miyazaki Hayato
This paper is concerned with time global behavior of solutions to nonlinear Schrödinger equation with a non-vanishing condition at the spatial infinity. Under a non-vanishing condition, it would be expected that the behavior is determined by the shape of the nonlinear term around the non-vanishing state. To observe this phenomenon, we introduce a generalized version of the Gross-Pitaevskii equation, which is a typical equation involving a non-vanishing condition, by modifying the shape of nonlinearity around the non-vanishing state. It turns out that, if the nonlinearity decays fast as a solution approaches to the non-vanishing state, then the equation admits a global solution which scatters to the non-vanishing element for both time directions.
