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<p>This study conducts a mathematical analysis of the (2+1)-dimensional Jaulent-Miodek (JM) equation, which is characterized by its energy-dependent Schrödinger potential. We utilize the Lie symmetry method to examine its integrability and solution framework, thereby deriving exact solutions. The invariance property of Lie groups has been used to generate infinitesimals, and therefore all potential vector fields, commutative relations and symmetry reductions are obtained systematically. The derived solutions contain several arbitrary constants and arbitrary function <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(f_1(t)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>f</mi> <mn>1</mn> </msub> <mrow> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation>, which have not been reported previously. These solutions offer profound insights into the propagation and interaction of nonlinear waves governed by the JM equation, enhancing the theoretical framework of soliton theory and its applications in mathematical physics and engineering. Moreover, the conserved vectors are developed inside the Lagrangian framework. The derived solutions are written in closed form and interpreted to bring out its physical significance. The physical evolution profile of these solutions is evidenced by numerical simulation that reveal a diverse array of soliton formation, including doubly soliton, multisoliton, as well as soliton fission and fusion phenomena. Consequently, a broader class of solutions is produced than those in previous works and shed more light on the dynamics governed by the JM equation.</p>

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Lie symmetries, similarity solutions and conservation laws of the (2+1)-dimensional Jaulent–Miodek equation

  • 期刊论文

  • 发表日期：

    2026年3月25日

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  • Anukriti,
  • Dig Vijay Tanwar

摘要

This study conducts a mathematical analysis of the (2+1)-dimensional Jaulent-Miodek (JM) equation, which is characterized by its energy-dependent Schrödinger potential. We utilize the Lie symmetry method to examine its integrability and solution framework, thereby deriving exact solutions. The invariance property of Lie groups has been used to generate infinitesimals, and therefore all potential vector fields, commutative relations and symmetry reductions are obtained systematically. The derived solutions contain several arbitrary constants and arbitrary function \(f_1(t)\) f 1 ( t ) , which have not been reported previously. These solutions offer profound insights into the propagation and interaction of nonlinear waves governed by the JM equation, enhancing the theoretical framework of soliton theory and its applications in mathematical physics and engineering. Moreover, the conserved vectors are developed inside the Lagrangian framework. The derived solutions are written in closed form and interpreted to bring out its physical significance. The physical evolution profile of these solutions is evidenced by numerical simulation that reveal a diverse array of soliton formation, including doubly soliton, multisoliton, as well as soliton fission and fusion phenomena. Consequently, a broader class of solutions is produced than those in previous works and shed more light on the dynamics governed by the JM equation.