Nonlinear Dynamics

, Volume 92, Issue 2, pp 781–792 | Cite as

Some group-invariant solutions of potential Kadomtsev–Petviashvili equation by using Lie symmetry approach

  • Mukesh Kumar
  • Atul Kumar Tiwari
Original Paper


A variety of closed-form solutions such as multiple-front wave, kink wave, waves interaction, curve-shaped multisoliton, parabolic and stationary wave solutions have been obtained by using invariance of the concerned potential Kadomtsev–Petviashvili (PKP) equation under the one-parameter Lie group of transformations. Lie symmetry transformations have been applied to generate various forms of invariant solutions of the PKP equation. The solutions provide extensive rich physical structure due to the existence of various arbitrary constants and functions. Results have been traced in context to spatiotemporal dynamics. Dynamic behavior of the results have been analyzed in terms of various wave propagations. Numerical simulation has been performed to obtain appropriate visual appearance of the traced solutions. The nature of solutions is investigated both analytically and physically through their evolutionary profiles by considering adequate choices of arbitrary functions and constants.


PKP equation Similarity method Soliton Multiple-front wave Invariant solutions 



The authors sincerely acknowledge the inputs provided by Dr. Tanuj Nandan, Associate Professor, School of Management Studies, MNNIT, Allahabad. One of the authors, Atul Kumar Tiwari, is grateful to CSIR-UGC, New Delhi, for the award of Senior Research Fellowship for writing this manuscript.


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© Springer Science+Business Media B.V., part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsMotilal Nehru National Institute of Technology AllahabadAllahabadIndia

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