Integrable discretization of coupled nonlinear Schrödinger equations

2000/02/25 by Takayuki Tsuchida · 2 citations
Physics and Astronomy · #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #Quantum Mechanics and Non-Hermitian Physics #nlin.SI

paper · pdf · doi:10.1016/s0034-4877(01)80032-x

published as Rep. Math. Phys. 46 (2000) 269-278 · 9 pages, LaTeX209 file, to appear in Proceedings of the XXXI Symposium on Mathematical Physics (Torun, Poland, May 1999), special issue of Reports on Mathematical Physics

arxiv created 2000/02/25 · openalex publication_date 2000/08/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

A discrete version of the inverse scattering method proposed by Ablowitz and Ladik is generalized to study an integrable full-discretization (discrete time and discrete space) of the coupled nonlinear Schrödinger equations. The generalization enables one to solve the initial-value problem. Soliton solutions and conserved quantities of the full-discrete system are constructed.

Citations

• Integrable semi-discretization of the coupled nonlinear Schrödinger equations

Cited by

• Novel periodic solutions and rogue waves of the defocusing scalar and coupled Ablowitz-Ladik systems on a nonzero background
• Soliton and breather interactions in the integrable discrete focusing Manakov system via Hirota's method