Interaction of modulated pulses in the nonlinear Schroedinger equation with periodic potential

2007/05/01 by Johannes Giannoulis, Alexander Mielke, Giannoulis, Johannes +3
Computer Science · Mathematics · Physics and Astronomy · #34E13 #34E20 #35Q55 #81Q20 #Analysis of PDEs (math.AP) #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Dynamics and Pattern Formation #Nonlinear Photonic Systems #Quantum optics and atomic interactions #math-ph #math.AP #math.MP #msc:34E13 #msc:34E20 #msc:35Q55 #msc:81Q20 #nlin.SI

paper · pdf · doi:10.48550/arxiv.0705.0131

arxiv created 2007/05/01 · openalex publication_date 2007/05/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider a cubic nonlinear Schroedinger equation with periodic potential. In a semiclassical scaling the nonlinear interaction of modulated pulses concentrated in one or several Bloch bands is studied. The notion of closed mode systems is introduced which allows for the rigorous derivation of a finite system of amplitude equations describing the macroscopic dynamics of these pulses.

Related

• Modulational instability for nonlinear Schrodinger equations with a periodic potential
• New approximation for nonlinear evolution in periodic potentials
• Nonlinear Schrödinger equations with exceptional potentials
• Justification of the Coupled Mode Asymptotics for Localized Wavepackets\n in the Periodic Nonlinear Schr "odinger Equation
• Classification of the minimal-mass blowup solutions to the two dimensional focusing cubic nonlinear Schrödinger system