Ordinary differential operators possessing invariant subspaces of polynomial type.

DOI10.1016/S1007-5704(03)00019-4zbMath1036.35014OpenAlexW2060091845MaRDI QIDQ1417835

Sergey R. Svirshchevskii

Publication date: 6 January 2004

Published in: Communications in Nonlinear Science and Numerical Simulation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s1007-5704(03)00019-4

zbMATH Keywords

evolution equationLie-Bäcklund symmetryhighest symmetry

Mathematics Subject Classification ID

Geometric theory, characteristics, transformations in context of PDEs (35A30) Nonlinear ordinary differential operators (34L30) Solutions to PDEs in closed form (35C05)

Related Items (4)

A refined invariant subspace method and applications to evolution equations ⋮ Invariant subspaces and exact solutions of a class of dispersive evolution equations ⋮ A class of third-order nonlinear evolution equations admitting invariant subspaces and associated reductions ⋮ Maximal dimension of invariant subspaces admitted by nonlinear vector differential operators

Cites Work

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• Symmetry and explicit solutions of partial differential equations
• Lie--Bäcklund symmetries of submaximal order of ordinary differential equations
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• EXACT MULTIDIMENSIONAL SOLUTIONS TO SOME NONLINEAR DIFFUSION EQUATIONS
• Invariant subspaces and new explicit solutions to evolution equations with quadratic nonlinearities
• Invariant Linear Spaces and Exact Solutions of Nonlinear Evolution Equations
• Invariant modules and the reduction of nonlinear partial differential equations to dynamical systems

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