Existence of bounds for dark solitons in a class of nonlinear Schrödinger equations: explicit upper and lower bounds

DOI10.1002/mma.2655zbMath1264.35206OpenAlexW2085021644MaRDI QIDQ4921734

Juan Belmonte-Beitia

Publication date: 13 May 2013

Published in: Mathematical Methods in the Applied Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/mma.2655

zbMATH Keywords

upper and lower solutionsheteroclinic orbitnonlinear Schrödinger equationsunstable manifolddark solitons

Mathematics Subject Classification ID

NLS equations (nonlinear Schrödinger equations) (35Q55) Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems (37K40) Homoclinic and heteroclinic orbits for dynamical systems (37C29) Soliton solutions (35C08)

Cites Work

• Explicit upper and lower bounds for the traveling wave solutions of Fisher-Kolmogorov type equations
• The nonlinear Schrödinger equation. Self-focusing and wave collapse
• Some results on homoclinic and heteroclinic connections in planar systems
• Nonlinear waves in Bose–Einstein condensates: physical relevance and mathematical techniques