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 ...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.展开更多
基金Supported by the National Natural Science Foundations of China under Grant Nos.11175092,11275123,11205092,and 10905038Talent FundK.C.Wong Magna Fund in Ningbo University
文摘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.
