Whitham hierarchy in growth problems
Copyright policy )Whitham hierarchy in growth problems
We discuss the recently established equivalence between the Laplacian growth in the limit of zero surface tension and the universal Whitham hierarchy known in soliton theory. This equivalence allows one to distinguish a class of exact solutions to the Laplacian growth problem in the multiply-connected case. These solutions corerespond to finite-dimensional reductions of the Whitham hierarchy representable as equations of hydrodynamic type which are solvable by means of the generalized hodograph method.
20 pages, 4 figures, based on the talk given at the Workshop ``Classical and quantum integrable systems'' (Dubna, January 2004), minor corrections
- Institute for Theoretical and Experimental Physics Russian Federation
High Energy Physics - Theory, Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests, Nonlinear Sciences - Exactly Solvable and Integrable Systems, Laplacian growth, Interface problems; diffusion-limited aggregation in time-dependent statistical mechanics, FOS: Physical sciences, Mathematical Physics (math-ph), Saffman-Taylor problem, Whitham equations, Other free boundary flows; Hele-Shaw flows, High Energy Physics - Theory (hep-th), Schwarz function, Lattice dynamics; integrable lattice equations, Exactly Solvable and Integrable Systems (nlin.SI), Mathematical Physics
High Energy Physics - Theory, Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests, Nonlinear Sciences - Exactly Solvable and Integrable Systems, Laplacian growth, Interface problems; diffusion-limited aggregation in time-dependent statistical mechanics, FOS: Physical sciences, Mathematical Physics (math-ph), Saffman-Taylor problem, Whitham equations, Other free boundary flows; Hele-Shaw flows, High Energy Physics - Theory (hep-th), Schwarz function, Lattice dynamics; integrable lattice equations, Exactly Solvable and Integrable Systems (nlin.SI), Mathematical Physics
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