Group Classification of Variable Coefficient $K\MakeLowercase{(m,n)}$ Equations

DOI10.7546/GIQ-15-2014-106-116zbMATH Open1316.82029arXiv1403.2545OpenAlexW4205209372MaRDI QIDQ4982821

Kyriakos Charalambous, Olena O. Vaneeva, C. Sophocleous

Publication date: 10 April 2015

Abstract: Lie symmetries of K(m,n) equations with time-dependent coefficients are classified. Group classification is presented up to widest possible equivalence groups, the usual equivalence group of the whole class for the general case and conditional equivalence groups for special values of the exponents m and n. Examples on reduction of K(m,n) equations (with initial and boundary conditions) to nonlinear ordinary differential equations (with initial conditions) are presented.

Full work available at URL: https://arxiv.org/abs/1403.2545

zbMATH Keywords

KdV equationLie symmetries\(K(m,n)\) equations

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Statistical mechanics of liquids (82D15)

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Preliminary group classification of equations v t t=f (x,v x)v x x+g(x,v x)

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