Painlevé test and exact similarity solutions of a class of nonlinear diffusion equations

DOI10.1063/1.529615zbMath0788.35108OpenAlexW2012045862MaRDI QIDQ4033952

Theo F. Nonnenmacher, Walter G. Glöckle, Gerd Baumann

Publication date: 16 May 1993

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

Full work available at URL: https://doi.org/10.1063/1.529615

zbMATH Keywords

similarity reductionsexact similarity solutionsinvariance of the Painlevé property

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Reaction-diffusion equations (35K57) Geometric theory, characteristics, transformations in context of PDEs (35A30) Correspondences and other transformation methods (e.g., Lie-Bäcklund) for PDEs on manifolds (58J72)

Related Items (2)

Singularity analysis and analytic solutions for the Benney-Gjevik equations ⋮ Integrability and a new breed of solitons of an NLS type equation in \(2+1\) dimensions

Cites Work

• Similarity solutions for nonlinear diffusion - A new integration procedure
• Similarity solutions for nonlinear diffusion - Further exact solutions
• Spatial distribution of dispersing animals
• Integrability of Hamiltonians with third- and fourth-degree polynomial potentials
• Exact similarity solutions to some nonlinear diffusion equations
• Singular point analysis and integrals of motion for coupled nonlinear Schrödinger equations
• New similarity reductions of the Boussinesq equation
• The Painlevé property for partial differential equations
• Lie transformations, similarity reduction, and solutions for the nonlinear Madelung fluid equations with external potential
• New classes of symmetries for partial differential equations
• A connection between nonlinear evolution equations and ordinary differential equations of P-type. I
• On the exactly solvable equation$S_t = [ ( \beta S + \gamma )^{ - 2} S_x _x + \alpha ( \beta S + \gamma )^{ - 2} S_x $ Occurring in Two-Phase Flow in Porous Media]
• When Nonlinear Differential Equations are Equivalent to Linear Differential Equations
• Isogroup and 'general' similarity solution of a nonlinear diffusion equation

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