增长问题中的Whitham层次
Whitham hierarchy in growth problems
摘要：
讨论了最近建立的零表面张力极限下的Laplacian增长与孤子理论中普遍的Whitham族之间的等价性。这种等价性使得我们可以区分多连通情形下拉普拉斯增长问题的一类精确解。这些解决方案corerespond有限维减少的Whitham层次表示为方程的流体动力学类型，这是可解的广义速端法。
英文摘要：
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.
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