Generation solutions algorithms for the class of inhomogeneous nonlinear diffusion equations

DOI10.1016/S0034-4877(11)80018-2zbMath1235.65100MaRDI QIDQ410686

O. V. Petrova, V. A. Tychynin

Publication date: 3 April 2012

Published in: Reports on Mathematical Physics (Search for Journal in Brave)

zbMATH Keywords

nonlinear superposition principleLie point symmetrynonlocal symmetriesformulae for generation of solutionsgeneralized hodograph transformation

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Reaction-diffusion equations (35K57) Numerical methods for ordinary differential equations (65L99)

Related Items (1)

Linearizability and nonlocal superposition for nonlinear transport equation with memory

Cites Work

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• Bäcklund transformations and their applications
• Use and construction of potential symmetries
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• Classification of potential symmetries of generalised inhomogeneous nonlinear diffusion equations
• The use of factors to discover potential systems or linearizations
• Symmetry classification using noncommutative invariant differential operators
• Nonlocal symmetries and generation of solutions for partial differential equations
• New results on group classification of nonlinear diffusion–convection equations
• New classes of symmetries for partial differential equations
• Potential symmetries of nonlinear diffusion - convection equations
• Potential symmetries of inhomogeneous nonlinear diffusion equations

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