Open AccessSYMMETRY REDUCTIONS OF WHITHAM-BROER-KAUP EQUATIONS IN SHALLOW WATER
Author(s) -
Hangyu Ruan,
Lou Sen-Yue
Publication year - 1992
Publication title -
wuli xuebao
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.199
H-Index - 47
ISSN - 1000-3290
DOI - 10.7498/aps.41.1213
Subject(s) - similarity (geometry) , logarithm , symmetry (geometry) , reduction (mathematics) , waves and shallow water , type (biology) , singularity , algebraic number , mathematics , mathematical physics , mathematical analysis , physics , geometry , computer science , thermodynamics , artificial intelligence , image (mathematics) , ecology , biology
In this paper, five types of similarity reductions of Whitham-Broer-kaup equations in shallow water are given by both the classical Lie approach and the direct method. The Painlevé Ⅱ type reduction equation obtained by the classical Lie approach is only the special case of that obtained by the direct method. In the similarity reduction results of the direct method, three types of singularity points, i.e., poles, algebraic branch points and logarithmic branch points. are included.