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<p>This research endeavours to analyse the symmetry reductions and exact solutions of the potential Kadomtsev–Petviashvili (PKP) equation by employing the similarity transformations method (STM), that relies on Lie group theory. The PKP equation delineates the dynamics of two-dimensional, finite-amplitude wave events that occur in plasma physics, hydrodynamics, and solid-state systems. The STM is consistently utilised to obtain similarity reductions of the PKP equation maintaining its invariance under continuous one-parameter Lie group transformations. Therefore, the reductions in the number of independent variables by enforcing the invariance of the governing equation under infinitesimal modifications and the test equation is converted into a system of ordinary differential equations (ODEs). The exact solutions of the resultant ODEs are subsequently derived under specific parametric conditions. The resultant solutions encompass arbitrary constants and functions <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="43538_2025_605_Article_IEq1.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="17" /> </InlineMediaObject> <EquationSource Format="TEX">\(f_4\)</EquationSource> </InlineEquation> and <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="43538_2025_605_Article_IEq2.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="17" /> </InlineMediaObject> <EquationSource Format="TEX">\(f_5\)</EquationSource> </InlineEquation>, providing significant generality and adaptability. These findings expand and generalise previously established solutions and, have not been documented in the literature. The physical significance and qualitative characteristics of the derived solutions, validated by numerical simulations, are assessed using graphical representations that depicts evolutionary nature, doubly soliton, multisoliton, line multisoliton and soliton annihilation nature. These findings highlight the efficacy and relevance of the suggested methodology in comprehending nonlinear wave dynamics dictated by the PKP equation.</p>

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On exact solutions and soliton nature of potential Kadomtsev-Petviashvili equation using Lie symmetry approach

  • 期刊论文

  • 发表日期：

    2025年11月17日

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  • Anukriti,
  • Dig Vijay Tanwar

摘要

This research endeavours to analyse the symmetry reductions and exact solutions of the potential Kadomtsev–Petviashvili (PKP) equation by employing the similarity transformations method (STM), that relies on Lie group theory. The PKP equation delineates the dynamics of two-dimensional, finite-amplitude wave events that occur in plasma physics, hydrodynamics, and solid-state systems. The STM is consistently utilised to obtain similarity reductions of the PKP equation maintaining its invariance under continuous one-parameter Lie group transformations. Therefore, the reductions in the number of independent variables by enforcing the invariance of the governing equation under infinitesimal modifications and the test equation is converted into a system of ordinary differential equations (ODEs). The exact solutions of the resultant ODEs are subsequently derived under specific parametric conditions. The resultant solutions encompass arbitrary constants and functions \(f_4\) and \(f_5\) , providing significant generality and adaptability. These findings expand and generalise previously established solutions and, have not been documented in the literature. The physical significance and qualitative characteristics of the derived solutions, validated by numerical simulations, are assessed using graphical representations that depicts evolutionary nature, doubly soliton, multisoliton, line multisoliton and soliton annihilation nature. These findings highlight the efficacy and relevance of the suggested methodology in comprehending nonlinear wave dynamics dictated by the PKP equation.