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<p>In this paper, we consider the stochastic modified Korteweg-de Vries-Zakharov-Kuznetsov (SmKdV-ZK) equation, which is driven in the Itô sense by advection noise. We show that by solving certain deterministic counterparts of the modified Korteweg-de Vries-Zakharov-Kuznetsov (for short DmKdV-ZK) with an extra diffusion term, and then merging the results with a solution of stochastic ordinary differential equations, the exact solution of the SmKdV-ZK equation may be discovered. We derive the soliton solutions for the DmKdV-ZK equation using two distinct methods: the extended tanh function method and the <InlineEquation ID="IEq1"> <EquationSource Format="MATHML"><math> <mo>exp</mo> <mo stretchy="false">(</mo> <mo>−</mo> <mi mathvariant="normal">Φ</mi> <mo stretchy="false">(</mo> <mi>η</mi> <mo stretchy="false">)</mo> <mo stretchy="false">)</mo> </math></EquationSource> <EquationSource Format="TEX">$\exp (-\Phi (\eta ))$</EquationSource> </InlineEquation>-expansion method. Moreover, we show how the advection noise impacts the solutions of the SmKdV-ZK equation by presenting several 3D graphs using a MATLAB software.</p>

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Exploration traveling solitary solutions to the mKdV-Zakharov-Kuznetsov equation with advection noise

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年3月13日

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  • Sofian T. Obeidat,
  • Doaa Rizk,
  • Wael W. Mohammed

摘要

In this paper, we consider the stochastic modified Korteweg-de Vries-Zakharov-Kuznetsov (SmKdV-ZK) equation, which is driven in the Itô sense by advection noise. We show that by solving certain deterministic counterparts of the modified Korteweg-de Vries-Zakharov-Kuznetsov (for short DmKdV-ZK) with an extra diffusion term, and then merging the results with a solution of stochastic ordinary differential equations, the exact solution of the SmKdV-ZK equation may be discovered. We derive the soliton solutions for the DmKdV-ZK equation using two distinct methods: the extended tanh function method and the exp ( − Φ ( η ) ) $\exp (-\Phi (\eta ))$ -expansion method. Moreover, we show how the advection noise impacts the solutions of the SmKdV-ZK equation by presenting several 3D graphs using a MATLAB software.