The classical, direct, and nonclassical methods for symmetry reductions of nonlinear partial differential equations

DOI10.4310/MAA.1997.v4.n2.a7zbMath0901.58069OpenAlexW2617378125MaRDI QIDQ1381216

Thomas J. Priestley, Peter A. Clarkson, David K. Ludlow

Publication date: 2 December 1998

Published in: Methods and Applications of Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.4310/maa.1997.v4.n2.a7

zbMATH Keywords

approximate solutions nonlinear partial differential equations exact analytical solutions Lie method shallow water wave equations infinitesimal transformations

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Applications of Lie groups to the sciences; explicit representations (22E70) Invariance and symmetry properties for PDEs on manifolds (58J70) Overdetermined problems for partial differential equations and systems of partial differential equations (35N99)

Related Items (6)

On some classes of free convection motions ⋮ Direct functional separation of variables and new exact solutions to axisymmetric unsteady boundary-layer equations ⋮ On the derivation of nonclassical symmetries of the Black-Scholes equation via an equivalence transformation ⋮ Functional separable solutions of nonlinear reaction-diffusion equations with variable coefficients ⋮ Symmetry reductions and new functional separable solutions of nonlinear Klein–Gordon and telegraph type equations ⋮ Nonclassical reductions of a \((3+1)\)-cubic nonlinear Schrödinger system

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