Hyperelliptic Solutions of KdV and KP equations: Reevaluation of Baker's Study on Hyperelliptic Sigma Functions
Matsutani, Shigeki
arXiv, 0007001 / Harvested from arXiv
Text on arXiv
Explicit function forms of hyperelliptic solutions of Korteweg-de Vries (KdV) and \break Kadomtsev-Petviashvili (KP) equations were constructed for a given curve $y^2 = f(x)$ whose genus is three. This study was based upon the fact that about one hundred years ago (Acta Math. (1903) {\bf{27}}, 135-156), H. F. Baker essentially derived KdV hierarchy and KP equation by using bilinear differential operator ${\bold{D}}$, identities of Pfaffians, symmetric functions, hyperelliptic $\sigma$-function and $\wp$-functions; $\wp_{\mu \nu} = -\partial_\mu \partial_\nu \log \sigma$ $= - ({\bold{D}}_\mu {\bold{D}}_\nu \sigma \sigma)/2\sigma^2$. The connection between his theory and the modern soliton theory was also discussed.
Publié le : 2000-07-01
Classification:  Nonlinear Sciences - Exactly Solvable and Integrable Systems,  Mathematical Physics 
@article{0007001,
     author = {Matsutani, Shigeki},
     title = {Hyperelliptic Solutions of KdV and KP equations: Reevaluation of Baker's
  Study on Hyperelliptic Sigma Functions},
     journal = {arXiv},
     volume = {2000},
     number = {0},
     year = {2000},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0007001}
}

Matsutani, Shigeki. Hyperelliptic Solutions of KdV and KP equations: Reevaluation of Baker's
  Study on Hyperelliptic Sigma Functions. arXiv, Tome 2000 (2000) no. 0, . http://gdmltest.u-ga.fr/item/0007001/