Open AccessCoupled KdV equation: similarity reduction and analytical solution
Author(s) -
Xiulan Cheng,
Jinyu Li,
Xue Jiang-Rong
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.60.110204
Subject(s) - korteweg–de vries equation , reduction (mathematics) , similarity (geometry) , integrable system , soliton , physics , mathematical physics , kadomtsev–petviashvili equation , dimensional reduction , similarity solution , mathematical analysis , mathematics , partial differential equation , characteristic equation , quantum mechanics , computer science , thermodynamics , nonlinear system , image (mathematics) , geometry , artificial intelligence , boundary layer
Using the CK direct method, we obtain the similarity reduction of coupled KdV equation, which is then explained in detail by group theory. To check the Painlev integrability of coupled KdV equation, the reduction equation is also classified by means of the Painlev test, and three types of P-integrable models are found. Finally, it is shown that the coupled KdV equation has kinds of traveling wave solutions, including conoidal periodic wave solution, soliton solution, and so on.