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<p>This work proposes deriving symmetry reductions and exact solutions for the (<InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(2+1\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>2</mn> <mo>+</mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation>)-modified Korteweg–de Vries–Kadomtsev–Petviashvili (mKdVKP) equation, which describes the velocity of the wave profile. New types of analytical solutions are developed and verified by comparing them with previously published results. Different kinds of exponential, rational, hyperbolic and trigonometric solutions are obtained. Animation profiles are plotted using MATLAB to demonstrate their physical importance. In every instance, the animation profile’s dominant dynamical behaviour is displayed. The velocity of the wave profile reveals bell-shaped to asymptotic, elastic single to multi-soliton, elastic multi-soliton, king-shaped to stationary, multi-soliton to stationary and multi-soliton to asymptotic behaviour. Additional research in this field may be suggested by the study’s trivially solved eqs 25 and 28.</p>

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Lie symmetries and invariant solutions of the (\(2+1\))-mKdVKP equation

  • 期刊论文

  • 发表日期：

    2026年5月6日

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  • Ravi Shankar Verma

摘要

This work proposes deriving symmetry reductions and exact solutions for the ( \(2+1\) 2 + 1 )-modified Korteweg–de Vries–Kadomtsev–Petviashvili (mKdVKP) equation, which describes the velocity of the wave profile. New types of analytical solutions are developed and verified by comparing them with previously published results. Different kinds of exponential, rational, hyperbolic and trigonometric solutions are obtained. Animation profiles are plotted using MATLAB to demonstrate their physical importance. In every instance, the animation profile’s dominant dynamical behaviour is displayed. The velocity of the wave profile reveals bell-shaped to asymptotic, elastic single to multi-soliton, elastic multi-soliton, king-shaped to stationary, multi-soliton to stationary and multi-soliton to asymptotic behaviour. Additional research in this field may be suggested by the study’s trivially solved eqs 25 and 28.