Nonisospectral scattering problems and similarity reductions

作者：Gordoa P R^*; Pickering A; Wattis J A D

来源：Applied Mathematics and Computation, 2014, 237: 77-84.

DOI：10.1016/j.amc.2014.03.107

• Korteweg-de Vries hierarchy
• Dispersive water wave hierarchy
• Nonisospectral scattering problems
• Similarity reductions
• Painleve hierarchies

We give mappings between hierarchies having nonisospectral scattering problems and hierarchies having isospectral scattering problems. Special cases of these changes of variables involve similarity variables, and similarity solutions of a hierarchy are seen to correspond to time-independent solutions of an equivalent hierarchy. We thus explain why the use of nonisospectral scattering problems and similarity reductions yield the same Painleve hierarchies. As examples we consider the Korteweg-de Vries hierarchy and the dispersive water wave hierarchy.

• 出版日期2014-6-15