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Investigation of a new similarity solution for the (2+1)-dimensional Schwarzian Korteweg–de Vries equation

    https://doi.org/10.1142/S0217984925500289Cited by:0 (Source: Crossref)

    We study the (2+1)-dimensional Schwarzian Korteweg–de Vries equation (SKdV). The explored solutions describe new Lump soliton colliding with visible soliton, an interaction between multi-soliton waves with one soliton, multi peaks of waves moving in a curved path, two hyperbolic waves moving together without interaction and some of periodic waves. We examine the commutative product between multi unknown Lie infinitesimals for the (2+1)-dimensional (SKdV) equation, and this study result in some new Lie vectors. The commutative product generates a system of nonlinear ODEs which had been solved manually. Through two stages of Lie symmetry reduction, SKdV equation is reduced to non-solvable nonlinear ODEs using various combinations of optimal Lie vectors. Using the Riccati–Bernoulli sub-ODE and Integration methods, we investigate new analytical solutions for these ODEs. Back substituting for the original variables generates new solutions for SKdV. Some selected solutions are illustrated through three-dimensional plots.

    PACS: 02.20.Sv, 02.30.Jr, 04.20.Jb, 05.45.Yv
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