Integrable boundary conditions for the nonlinear Schrödinger hierarchy

2025/02/28 by Baoqiang Xia, Xia, Baoqiang · 1 voice
Physics and Astronomy · #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #nlin.SI

paper · pdf · doi:10.48550/arxiv.2502.21052

Abstract

We study integrable boundary conditions associated with the whole hierarchy of nonlinear Schrödinger (NLS) equations defined on the half-line. We find that the even order NLS equations and the odd order NLS equations admit rather different integrable boundary conditions. In particular, the odd order NLS equations permit a new class of integrable boundary conditions that involves the time reversal. We prove the integrability of the NLS hierarchy in the presence of our new boundary conditions in the sense that the models possess infinitely many integrals of the motion in involution. Moreover, we develop further the boundary dressing technique to construct soliton solutions for our new boundary value problems.

Discussions

• Baoqiang Xia: Integrable boundary conditions for the nonlinear Schr\"{o}dinger hierarchy https://arxiv.org/abs/2502.21052 https://arxiv.org/pdf/2502.21052 https://arxiv.org/html/2502.21052 [bsky, 0 points, 1 comments]

Related

• An integrable generalization of the nonlinear Schrödinger equation on the half-line and solitons
• On the nonlinear Schrödinger equation with a time-dependent boundary condition
• A type I defect and new integrable boundary conditions for the coupled nonlinear Schrödinger equation
• Dressing the boundary: on soliton solutions of the nonlinear Schrödinger equation on the half-line
• Vector NLS solitons interacting with a boundary