Additional symmetries of the nonlinear Schrödinger equation

DOI10.1007/BF01017968zbMath0596.35082OpenAlexW2023525415MaRDI QIDQ1078412

E. I. Shul'man, Alexander Yu. Orlov

Publication date: 1985

Published in: Theoretical and Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01017968

zbMATH Keywords

one-dimensional nonlinear evolution equationsnonlinear Schrödinger equationinverse scattering methodconformal algebragenerators of symmetries

Mathematics Subject Classification ID

Scattering theory for PDEs (35P25) First-order nonlinear hyperbolic equations (35L60) Partial differential equations of mathematical physics and other areas of application (35Q99)

Related Items (10)

Non-autonomous reductions of the KdV equation and multi-component analogs of the Painlevé equations P34 and P3 ⋮ The ghost symmetries of the q-KP hierarchy ⋮ Nonautonomous symmetries of the KdV equation and step-like solutions ⋮ Virasoro symmetries of multicomponent Gelfand-Dickey systems ⋮ On analogs of wave catastrophe functions that are solutions of nonlinear integrable equations ⋮ Algebra of pseudodifferential operators and symmetries of equations in the Kadomtsev–Petviashvili hierarchy ⋮ Symmetries of the Hirota difference equation ⋮ A multiple scales approach to maximal superintegrability ⋮ Supersymmetric Kadomtsev–Petviashvili hierarchy: “Ghost” symmetry structure, reductions, and Darboux–Bäcklund solutions ⋮ Higher Order Quantum Superintegrability: A New “Painlevé Conjecture”

Cites Work

• On a trace functional for formal pseudo-differential operators and the symplectic structure of the Korteweg-deVries type equations
• Modified fourth-order Casimir invariants and indices for simple Lie algebras

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