Maximal dimension of invariant subspaces admitted by nonlinear vector differential operators

DOI10.1063/1.3574534zbMath1316.34092OpenAlexW1991070953MaRDI QIDQ5263580

Chunrong Zhu, Chang-Zheng Qu

Publication date: 17 July 2015

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

Full work available at URL: https://doi.org/10.1063/1.3574534

Mathematics Subject Classification ID

Several-variable operator theory (spectral, Fredholm, etc.) (47A13) Invariant subspaces of linear operators (47A15) Nonlinear ordinary differential operators (34L30)

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Cites Work

• Unnamed Item
• Unnamed Item
• Nonlinear differential operators of first and second order possessing invariant linear spaces of maximal dimension
• Structure theorems for linear and nonlinear differential operators admitting invariant polynomial subspaces
• On new exact blow-up solutions for nonlinear heat conduction equations with source and applications
• Ordinary differential operators possessing invariant subspaces of polynomial type.
• A stability technique for evolution partial differential equations. A dynamical systems approach
• Separation of variables and exact solutions to quasilinear diffusion equations with nonlinear source
• Exact solutions and invariant spaces for nonlinear gradient diffusion equations
• On invariant sets and explicit solutions of nonlinear evolution equations with quadratic nonlinearities
• Lie-Bäcklund symmetries of linear ODEs and generalized separation of variables in nonlinear equations
• Exact polynomial solutions to some nonlinear diffusion equations
• Classification of coupled systems with two-component nonlinear diffusion equations by the invariant subspace method
• Invariant sets of evolution equations
• Lie algebras and polynomials in one variable
• On invariant subspaces for nonlinear finite-difference operators
• A symmetry test for quasilinear coupled systems
• Reductions and exact solutions of some nonlinear partial differential equations under four types of generalized conditional symmetries
• Exact solutions to nonlinear diffusion equations obtained by a generalized conditional symmetry method
• EXACT MULTIDIMENSIONAL SOLUTIONS TO SOME NONLINEAR DIFFUSION EQUATIONS
• Group Classification and Generalized Conditional Symmetry Reduction of the Nonlinear Diffusion–Convection Equation with a Nonlinear Source
• Nonlinear interaction of traveling waves of nonintegrable equations
• Conditional Lie-Backlund symmetry and reduction of evolution equations
• Invariant solutions of two models of evolution of turbulent bursts
• 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
• Conditional Lie Bäcklund Symmetries and Sign‐Invariants to Quasi‐Linear Diffusion Equations

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