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<p>This study investigates an extended <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\((2+1)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <mn>2</mn> <mo>+</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>-dimensional nonlinear evolution equation with time-dependent coefficients that describe nonlinear wave dynamics in variable environments. While previous studies predominantly considered cases of constant-coefficients, we investigate how temporal variability influences the formation and dynamics of nonlinear structures. By applying the Wronskian technique, we establish explicit Wronskian solutions and derive general <i>N</i>-soliton and resonant Y-type soliton configurations. Using a symbolic-computation-based bilinear approach combined with the variable transformation <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(X=x-\omega {(t)}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>X</mi> <mo>=</mo> <mi>x</mi> <mo>-</mo> <mi>ω</mi> <mrow> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation>, we further construct higher-order rational solutions that capture both soliton and rogue-wave behavior. Introducing two free parameters <InlineEquation ID="IEq6"> <EquationSource Format="TEX">\(\alpha \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>α</mi> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq7"> <EquationSource Format="TEX">\(\beta \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>β</mi> </math></EquationSource> </InlineEquation>, enables the generation of tunable rogue-wave patterns with controllable center locations. The results highlight new interaction phenomena and reveal the significant role played by time-dependent coefficients in shaping the evolution of solitons and rogue waves, offering insights applicable to fluid dynamics, optics, and plasma systems.</p>

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Wronskian and rational solutions of a \((2+1)\)-dimensional nonlinear evolution equation with time-dependent coefficients

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年2月25日

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  • Majid Madadi,
  • Lanre Akinyemi,
  • Kamyar Hosseini

摘要

This study investigates an extended \((2+1)\) ( 2 + 1 ) -dimensional nonlinear evolution equation with time-dependent coefficients that describe nonlinear wave dynamics in variable environments. While previous studies predominantly considered cases of constant-coefficients, we investigate how temporal variability influences the formation and dynamics of nonlinear structures. By applying the Wronskian technique, we establish explicit Wronskian solutions and derive general N-soliton and resonant Y-type soliton configurations. Using a symbolic-computation-based bilinear approach combined with the variable transformation \(X=x-\omega {(t)}\) X = x - ω ( t ) , we further construct higher-order rational solutions that capture both soliton and rogue-wave behavior. Introducing two free parameters \(\alpha \) α and \(\beta \) β , enables the generation of tunable rogue-wave patterns with controllable center locations. The results highlight new interaction phenomena and reveal the significant role played by time-dependent coefficients in shaping the evolution of solitons and rogue waves, offering insights applicable to fluid dynamics, optics, and plasma systems.