On the nonlinear Schrödinger equation with a time-dependent boundary condition

Abstract

We study the nonlinear Schrödinger equation on the half-line with a boundary condition that involves time derivative. This boundary condition was presented by Zambon [J. High Energ. Phys. 2014 (2014) 36]. We establish the integrability of such a boundary both by using the Sklyanin's formalism and by using the tool of Bäcklund transformations together with a suitable reduction of reflection type. Moreover, we present a method to derive explicit formulae for multi-soliton solutions of the boundary problem by virtue of the Darboux transformation method in conjunction with a boundary dressing technique.

References in corpus (8)

• Classically integrable field theories with defects
• Quantum and classical integrable sine-Gordon model with defect
• Solitons, boundary value problems and a nonlinear method of images
• Liouville integrable defects: the non-linear Schrodinger paradigm
• A multisymplectic approach to defects in integrable classical field theory
• Classical integrable defects as quasi Bäcklund transformations
• New integrable boundary conditions for the Ablowitz-Ladik model: from Hamiltonian formalism to nonlinear mirror image method
• Type I integrable defects and finite-gap solutions for KdV and sine-Gordon models