A Tree of Linearisable Second-Order Evolution Equations by Generalised Hodograph Transformations

DOI10.2991/jnmp.2001.8.3.3zbMath0997.35093arXivnlin/0201040OpenAlexW2154421324MaRDI QIDQ2744649

Marianna Euler, Norbert Euler

Publication date: 4 July 2002

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

Full work available at URL: https://arxiv.org/abs/nlin/0201040

zbMATH Keywords

hierarchy of evolution equationsgeneralised 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)

Related Items

On Nonlocal Symmetries, Nonlocal Conservation Laws and Nonlocal Transformations of Evolution Equations: Two Linearisable Hierarchies ⋮ Hodograph-type transformations ⋮ Hodograph-Type Transformations for Linearization of Systems of Nonlinear Diffusion Equations ⋮ Hodograph Transformations and Cauchy Problem to Systems of Nonlinear Parabolic Equations ⋮ A Nonlinearly Dispersive Fifth Order Integrable Equation and its Hierarchy ⋮ \({\lambda}\)-symmetries of some chains of ordinary differential equations ⋮ Reciprocal Bäcklund transformations of autonomous evolution equations

Cites Work

• Evolutionary equations with nontrivial Lie-Bäcklund group
• Hodograph Transformations of Linearizable Partial Differential Equations
• A symmetry approach to exactly solvable evolution equations
• 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]
• Auto-hodograph transformations for a hierarchy of nonlinear evolution equations
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