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Pure Mathematics 2025
(2 + 1)维BLMP方程Lump波与孤波的相互作用解
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Abstract:
本文应用Hirota双线性方法探讨了(2 + 1)维Boiti-Leon-Manna-Pempinelli (BLMP)方程的解及其相互作用。该方法的一个特点是使用对数变换将方程转化为双线性形式，且我们在对数变换中引入了非零常数。本文分析了1-lump波分别与1-kink孤波和2-kink孤波之间的相互作用，揭示了它们的弹性和共振碰撞行为。为了进一步说明这些解的特征，我们利用Mathematica软件提供了详细的三维图示结果。
In this study, we investigate the (2 + 1)-dimensional Boiti-Leon-Manna-Pempinelli equations using the Hirota bilinear method. A feature of our approach is the use of a logarithmic transformation to convert the equation into bilinear form with the introduction of a nonzero constant in the transformation. We analyze the interaction dynamics of lump solutions with one and two kink solitons, revealing their elastic and resonant collision behaviors. To further illustrate the characteristics of these solutions, we provide detailed 3D plots using the Mathematica software.
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