Rogue Wave And Breather Solutions For Several High-dimensional Nonlinear Wave Equations

In this paper,solutions of high-dimensional nonlinear wave equations are studied by means of the symbolic computing system Mathematica.The high-order rogue wave solutions,breather solutions,interaction solutions and rational solutions of several high-dimensional nonlinear wave equations are constructed by two symbolic computation approaches,the Hirota direct method and the generalized Darboux transformation method.The main work is as follows:(1)Applying the first symbolic computation approach,the high-order rogue wave solutions of the(3+1)-dimensional Kadomtsev-Petviashvili I(KP I)equation and the(2+1)-dimensional generalized Camassa-Holm-KP(CH-KP)equation are obtained.By extending the real parameters of the Hirota direct method to the complex,breather solutions and interaction solutions of the(3+1)-dimensional KP I equation are constructed.(2)Based on the first symbolic computation approach,the auxiliary function is generalized to the general polynomial form and hence the second symbolic computation approach is given.By the second symbolic computation approach and the Hirota direct method,the high-order rogue wave solutions,breather solutions and interaction solutions of the(3+1)-dimensional extended Jimbo-Miwa(JM)equation are obtained.(3)On the basis of the usual Darboux transformation,the Mn),(-fold generalized Darboux transformation are constructed by taking the limit of Taylor expansion of Darboux matrix.And using the generalized Darboux transformation,the higher-order rational and rogue wave solutions of a(3+1)-dimensional nonlinear evolution equation are obtained.