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Title: Symmetry solutions and conserved vectors of the two-dimensional Korteweg-de Vries equation.
Authors: Plaatjie, Karabo.
Motsepa, Tanki.
Johnpillai, A. G.
Khalique, Chaudry Masood.
North-West University
School of Computing and Mathematical Sciences
Eastern University
North-West University
Keywords: Two-dimensional Korteweg-de Vries equation.;Lie point symmetries.;Exact solution.;Conservation laws.;Multiplier method.
Issue Date: 2022
Publisher: Springer Science and Business Media {LLC}
Abstract: We study the two-dimensional constant coefficients Korteweg-de Vries equation, which was established not long ago in the literature. We construct group-invariant solutions and conservation laws for this equation. Lie group method is applied and the Lie point symmetries are derived. We show how one can derive travelling waves symmetry solutions given in respect of the Weierstrass-zeta and hyperbolic functions using its symmetries. Furthermore, we present infinite number of conservation laws of the underlying equation obtained by means of the multiplier approach.
DOI: 10.1007/s40819-022-01428-9
Appears in Collections:Journal articles

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