摘要
A consistent tanh expansion(CTE) method is developed for the dispersion water wave(DWW) system. For the CTE solvable DWW system, there are two branches related to tanh expansion, the main branch is consistent while the auxiliary branch is not consistent. From the consistent branch, we can obtain infinitely many exact significant solutions including the soliton-resonant solutions and soliton-periodic wave interactions. From the inconsistent branch, only one special solution can be found. The CTE related nonlocal symmetries are also proposed. The nonlocal symmetries can be localized to find finite B¨acklund transformations by prolonging the model to an enlarged one.
A consistent tanh expansion （CTE） method is developed for the dispersion water wave （DWW） system. For the CTE solvable DlVVC system, there are two branches related to tanh expansion, the main branch is consistent while the auxiliary branch is not consistent. From the consistent branch, we can obtain infinitely many exact significant solutions including the soliton-resonant solutions and soliton-periodic wave interactions. From the inconsistent branch, only one special solution can be found. The CTE related nonlocal symmetries are also proposed. The nonlocai symmetries can be localized to find finite Backlund transformations by prolonging the model to an enlarged one.
基金
Supported by the National Natural Science Foundations of China under Grant Nos.11175092,11275123,11205092,and 10905038
Talent Fund
K.C.Wong Magna Fund in Ningbo University
关键词
局域对称性
C系统
可解性
CTE
水波
色散
BACKLUND变换
精确解
consistent tanh expansion, dispersion water wave （DWW） system, nonlocal symmetries, the con-sistent Riccati expansion
