Traveling Solitary Waves in the Periodic Nonlinear Schrödinger Equation with Finite Band Potentials

DOI10.1137/130933149zbMath1301.35149arXiv1305.3504OpenAlexW2003241253MaRDI QIDQ5495227

Tomáš Dohnal

Publication date: 31 July 2014

Published in: SIAM Journal on Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1305.3504

zbMATH Keywords

nonlinear Schrödinger equationGross-Pitaevskii equationcoupled mode equationsenvelope approximationLamé's equationfinite band potentialmoving gap solitonperiodic structure with finite contrast

Mathematics Subject Classification ID

Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (41A60) NLS equations (nonlinear Schrödinger equations) (35Q55) Asymptotic expansions of solutions to PDEs (35C20) Soliton equations (35Q51) Soliton solutions (35C08)

Related Items (4)

Bifurcation of nonlinear Bloch waves from the spectrum in the Gross-Pitaevskii equation ⋮ Bifurcation of gap solitons in coupled mode equations in \(d\) dimensions ⋮ Coupled mode equations and gap solitons in higher dimensions ⋮ Justification of the coupled mode asymptotics for localized wavepackets in the periodic nonlinear Schrödinger equation

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