Open AccessNew type infinite sequence exact solutions of the second KdV equation with variable coefficients
Author(s) -
Taogetusang,
Yang Bai
Publication year - 2012
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.61.060201
Subject(s) - sequence (biology) , korteweg–de vries equation , transformation (genetics) , variable (mathematics) , soliton , exact solutions in general relativity , nonlinear system , type (biology) , computation , mathematics , symbolic computation , mathematical analysis , physics , algorithm , quantum mechanics , ecology , biochemistry , chemistry , genetics , gene , biology
To construct a number of new infinite sequence exact solutions of nonlinear evolution equations and to study the two characteristics of constructivity and mechanicalness of the first kind of elliptic equation, new types of solutions and the corresponding Bcklund transformation of the equation are presented. Then the second kind of KdV equation with variable coefficients is chosen as a practical example and three kinds of new infinite sequence exact solutions are obtained with the help of symbolic computation system Mathematica, where are included the smooth soliton-like solutions, the infinite sequence peak soliton solutions, and the infinite sequence compact soliton solutions. The method can be used to search for new infinite sequence exact solutions of other nonlinear evolution equations with variable coefficients.