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arXiv · 2407.06916

Action-angle variables for the nonlinear Schr\"{o}dinger equation on the half-line

Baoqiang Xia
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Abstract

We consider the nonlinear Schr\"{o}dinger (NLS) equation on the half-line subjecting to a class of boundary conditions preserve the integrability of the model. For such a half-line problem, the Poisson brackets of the corresponding scattering data are computed, and the variables of action-angle type are constructed. These action-angle variables completely trivialize the dynamics of the NLS equation on the half-line.

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Baoqiang Xia. 2024-07-09. Action-angle variables for the nonlinear Schr\"{o}dinger equation on the half-line. https://arxiv.org/abs/2407.06916

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