Semiclassical Solutions of the Nonlinear Schrödinger Equation

DOI10.2991/JNMP.1999.6.2.2zbMath0947.35152arXivmath/9904189OpenAlexW2066420416MaRDI QIDQ4498255

A. Yu. Trifonov, Alexander Shapovalov

Publication date: 15 August 2000

Published in: Journal of Nonlinear Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/9904189

zbMATH Keywords

nonlinear Schrödinger equationasymptotic WKB-solutionmultidimensional solitary wavessemiclassically concentrated solutions

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) NLS equations (nonlinear Schrödinger equations) (35Q55) Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems (37K40)

Related Items (1)

A semiclassical approximation for the nonstationary two-dimensional nonlinear Schrödinger equation with an external field in polar coordinates

Cites Work

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• Semiclassical trajectory-coherent approximation in quantum mechanics. I: High-order corrections to multidimensional time-dependent equations of Schrödinger type
• Self-dual Yang-Mills fields in \(d=4\) and integrable systems in \(1\leq d\leq 3\)
• Aspects of Semiclassical Theory in the Presence of Classical Chaos
• Integrable heterogeneous nonlinear Schrödinger equations with dielectric loss: Lie–Bäcklund symmetries
• Soliton solutions to the gauged nonlinear Schrödinger equation on the plane
• Nonlinear Schrodinger solitons in the presence of an external potential

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