1-Multisoliton and other invariant solutions of combined KdV - nKdV\n equation by using symmetry approach

2018/05/28 by Sachin Kumar, Dharmendra Kumar, Kumar, Sachin +1
Mathematics · Physics and Astronomy · #35B06 #35C05 #76M60 #Algebraic structures and combinatorial models #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Photonic Systems #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.1805.10983

openalex publication_date 2018/05/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Lie symmetry method is applied to investigate symmetries of the combined\nKdV-nKdV equation, that is a new integrable equation by combining the KdV\nequation and negative order KdV equation. Symmetries which are obtained in this\narticle, are further helpful for reducing the combined KdV-nKdV equation into\nordinary differential equation. Moreover, a set of eight invariant solutions\nfor combined KdV-nKdV equation is obtained by using proposed method. Out of the\neight solutions so obtained in which two solutions generate progressive wave\nsolutions, five are singular solutions and one multisoliton solutions which is\nin terms of WeierstrassZeta function.\n

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