Kadomtsev-Petviashvili system and reduction: generalized Cauchy matrix approach

Song-lin Zhao; Shou-feng Shen; Wei Feng

Kadomtsev-Petviashvili system and reduction: generalized Cauchy matrix approach

Exactly Solvable and Integrable Systems 2014-10-17 v3

Authors: Song-lin Zhao , Shou-feng Shen , Wei Feng

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 $\tau$ -function by $\tau=|\bI+\bM\bC|$ . With the help of some recurrence relations, the reduction to Korteweg-de Vries system, Boussinesq system and extended Boussinesq system are also discussed.

Keywords

Kadomtsev-Petviashvili system generalized Cauchy matrix approach Sylvester equation exact solutions tau-function reduction Korteweg-de Vries system Boussinesq system

Cite

@article{arxiv.1404.3043,
  title  = {Kadomtsev-Petviashvili system and reduction: generalized Cauchy matrix approach},
  author = {Song-lin Zhao and Shou-feng Shen and Wei Feng},
  journal= {arXiv preprint arXiv:1404.3043},
  year   = {2014}
}

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23 pages, minor revisions and one ref added

Kadomtsev-Petviashvili system and reduction: generalized Cauchy matrix approach

Abstract

Keywords

Cite

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