Diffusion equations and Lie and Lie-Bäcklund transformation groups

DOI10.1016/0378-4371(82)90266-7zbMath0513.58045OpenAlexW1990017379WikidataQ115363225 ScholiaQ115363225MaRDI QIDQ1050690

Walter Strampp, Willi-Hans Steeb

Publication date: 1982

Published in: Physica A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0378-4371(82)90266-7

zbMATH Keywords

conservation lawssymmetry groupssimilarity solutionsconserved currentsNoether's theoremLie and Lie-Bäcklund transformation groupslinear and nonlinear diffusion equations

Mathematics Subject Classification ID

Applications of Lie groups to the sciences; explicit representations (22E70) Jets in global analysis (58A20) Diffusion processes and stochastic analysis on manifolds (58J65)

Related Items

Sinh-Gordon equation, Painlevé property and Bäcklund transformation, Double reduction of PDEs from the association of symmetries with conservation laws with applications, On the integrability of nonlinear Dirac equations, Symmetry vector fields and similarity solutions of a nonlinear field equation describing the relaxation to a Maxwell distribution, Generalization of the double reduction theory, On Lie–Bäcklund vector fields of the evolution equations ∂2u/∂x ∂t=f(u) and ∂u/∂t=∂2u/∂x2+f(u)

Cites Work

• Symmetries of non-linear reaction-diffusion equations and their solutions
• Symmetry, conserved quantities and moments in diffusive equations
• On the remarkable nonlinear diffusion equation (∂/∂x)[a (u+b)−2(∂u/∂x)−(∂u/∂t)=0]
• Group Transformations and the Nonlinear Heat Diffusion Equation