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首页> 外文期刊>Mathematical modelling of natural phenomena >Exactly Solvable Models and Bifurcations:the Case of the Cubic NLS with a δ or a δ' Interaction in Dimension One
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Exactly Solvable Models and Bifurcations:the Case of the Cubic NLS with a δ or a δ' Interaction in Dimension One

机译：完全可解的模型和分支：一维具有δ或δ'相互作用的立方NLS的情况

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摘要

We explicitly give all stationary solutions to the focusing cubic NLS on the line, in the presence of a defect of the type Dirac's delta or delta prime. The models prove interesting for two features:first, they are exactly solvable and all quantities can be expressed in terms of elementary functions. Second, the associated dynamics is far from being trivial. In particular, the NLS with a delta prime potential shows two symmetry breaking bifurcations:the first concerns the ground state and was already known. The second emerges on the first excited state, and up to now had not been revealed. We highlight such bifurcations by computing the nonlinear and the no-defect limits of the stationary solutions.
机译：在存在狄拉克三角洲或三角洲素数类型的缺陷的情况下，我们将所有固定解明确地给予线上的聚焦三次NLS。该模型具有两个有趣的特征：首先，它们可以完全求解，并且所有数量都可以用基本函数表示。其次，相关的动态绝非易事。特别是，具有三角形素数电势的NLS表现出两个对称的断裂分支：第一个涉及基态，并且已经为人所知。第二个出现在第一个兴奋状态，到目前为止尚未发现。我们通过计算固定解的非线性和无缺陷极限来突出这种分叉。

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