Laplacian Growth and Whitham Equations of Soliton Theory
Krichever, I. ; Mineev-Weinstein, M. ; Wiegmann, P. ; Zabrodin, A.
arXiv, 0311005 / Harvested from arXiv
Text on arXiv
The Laplacian growth (the Hele-Shaw problem) of multi-connected domains in the case of zero surface tension is proven to be equivalent to an integrable systems of Whitham equations known in soliton theory. The Whitham equations describe slowly modulated periodic solutions of integrable hierarchies of nonlinear differential equations. Through this connection the Laplacian growth is understood as a flow in the moduli space of Riemann surfaces.
Publié le : 2003-11-03
Classification:  Nonlinear Sciences - Exactly Solvable and Integrable Systems,  High Energy Physics - Theory,  Mathematical Physics,  Nonlinear Sciences - Pattern Formation and Solitons 
@article{0311005,
     author = {Krichever, I. and Mineev-Weinstein, M. and Wiegmann, P. and Zabrodin, A.},
     title = {Laplacian Growth and Whitham Equations of Soliton Theory},
     journal = {arXiv},
     volume = {2003},
     number = {0},
     year = {2003},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0311005}
}

Krichever, I.; Mineev-Weinstein, M.; Wiegmann, P.; Zabrodin, A. Laplacian Growth and Whitham Equations of Soliton Theory. arXiv, Tome 2003 (2003) no. 0, . http://gdmltest.u-ga.fr/item/0311005/