Open AccessThe single solitary wave with double kinks of the combined KdV equation and its stability
Author(s) -
Shi Yu-Ren,
Juan Zhang,
Yang Hong-Juan,
Wen-Shan Duan
Publication year - 2011
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.60.020402
Subject(s) - korteweg–de vries equation , hyperbola , soliton , stability (learning theory) , physics , type (biology) , mathematical analysis , function (biology) , traveling wave , mathematical physics , classical mechanics , nonlinear system , mathematics , quantum mechanics , computer science , geometry , ecology , machine learning , evolutionary biology , biology
Based on the ideas of the hyperbola function expansion method, we obtained some analytical solutions of the combined KdV-mKdV (cKdV) equations by introducing new expansion functions.One of the single soliton solutions has the kink-antikink structure, and this solution reduces to the kink-like solution and the bell-like solution under different limitations. Theoretical analysis shows that the cKdV equation has both propagated-type and non-propagated-type solitary wave solutions. We also investigated the stability of the single solitary wave solution with double kinks numerically. The results indicate that the solution may be stable or unstable, depending on different sets of parameters.