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arXiv · 1404.3043

Kadomtsev-Petviashvili system and reduction: generalized Cauchy matrix approach

Song-lin Zhao·Shou-feng Shen·Wei Feng
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Abstract

By the Sylvester equation $\bL\bM-\bM\bK=\br\bs^{\st}$ together with an evolution equation set of $\br$ and $\bs$, generalized Cauchy matrix approach is established to investigate exact solutions for Kadomtsev-Petviashvili system, including Kadomtsev-Petviashvili equation, modified Kadomtsev-Petviashvili equation and Schwarzian Kadomtsev-Petviashvili equation. The matrix $\bM$ provides $τ$-function by $τ=|\bI+\bM\bC|$. With the help of some recurrence relations, the reduction to Korteweg-de Vries system, Boussinesq system and extended Boussinesq system are also discussed.

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Song-lin Zhao, Shou-feng Shen, Wei Feng. 2014-10-16. Kadomtsev-Petviashvili system and reduction: generalized Cauchy matrix approach. https://arxiv.org/abs/1404.3043

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