Higher symmetries and exact solutions of linear and nonlinear Schrödinger equation

DOI10.1063/1.532180zbMath0890.35143OpenAlexW2171193308MaRDI QIDQ4378333

W. I. Fushchich, Anatolia G. Nikitin

Publication date: 29 June 1998

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

Full work available at URL: https://semanticscholar.org/paper/e4b0111bb4f6fb612f5ffe4d97c1939008034a0a

zbMATH Keywords

reductionsnonlinear Schrödinger equationsconditional symmetrieshigher symmetries of the Schrödinger equation

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) Invariance and symmetry properties for PDEs on manifolds (58J70) Geometric theory, characteristics, transformations in context of PDEs (35A30) Solutions to PDEs in closed form (35C05)

Related Items (14)

Nonlinear supersymmetry in quantum mechanics: algebraic properties and differential repre\-sentation ⋮ Two-dimensional superintegrable systems from operator algebras in one dimension ⋮ On covariant realizations of the Poincaré group \(P(1,3)\) ⋮ Kinematical invariance groups of the 3d Schrödinger equations with position dependent masses ⋮ Fourth order superintegrable systems separating in polar coordinates. I. Exotic potentials ⋮ Superintegrability with third order integrals of motion, cubic algebras, and supersymmetric quantum mechanics. II. Painlevé transcendent potentials ⋮ Systems of reaction diffusion equations and their symmetry properties ⋮ Symmetries of the Schrödinger–Pauli equation for neutral particles ⋮ Connection between quantum systems involving the fourth Painlevé transcendent and k-step rational extensions of the harmonic oscillator related to Hermite exceptional orthogonal polynomial ⋮ Group classification of Schrödinger equations with position dependent mass ⋮ Classical ladder operators, polynomial Poisson algebras, and classification of superintegrable systems ⋮ Fundamental Solution of the Volkov Problem (Characteristic Representation) ⋮ A precise definition of reduction of partial differential equations ⋮ New infinite families of Nth-order superintegrable systems separating in Cartesian coordinates

Cites Work

• The complete set of symmetry operators of the Schrödinger equation
• Higher symmetries of the Schrödinger equation
• Equations of long waves with a free surface. II: Hamiltonian structure and higher equations
• The construction of special solutions to partial differential equations
• MORE ON SUPERSYMMETRIES OF THE SCHRÖDINGER EQUATION
• MORE ON PARASUPERSYMMETRIES OF THE SCHRÖDINGER EQUATION
• Non-factorizable separable systems and higher-order symmetries of the Dirac operator
• New similarity reductions of the Boussinesq equation
• On the new invariance algebras and superalgebras of relativistic wave equations
• More on symmetries of the Schrodinger equation
• Korteweg-de Vries Equation and Generalizations. I. A Remarkable Explicit Nonlinear Transformation

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