In this paper, the evolutionary behavior of N-solitons for a (2 + 1)-dimensional Konopelchenko-Dubrovsky equations is studied by using the Hirota bilinear method and the long wave limit method. Based on the N-soliton ...In this paper, the evolutionary behavior of N-solitons for a (2 + 1)-dimensional Konopelchenko-Dubrovsky equations is studied by using the Hirota bilinear method and the long wave limit method. Based on the N-soliton solution, we first study the evolution from N-soliton to T-order (T=1,2) breather wave solutions via the paired-complexification of parameters, and then we get the N-order rational solutions, M-order (M=1,2) lump solutions, and the hybrid behavior between a variety of different types of solitons combined with the parameter limit technique and the paired-complexification of parameters. Meanwhile, we also provide a large number of three-dimensional figures in order to better show the degeneration of the N-soliton and the interaction behavior between different N-solitons.展开更多
In this paper,we are concerned with the existence of nontrivial solutions to a 2m-order nonlinear periodic boundary value problem.By the infinite dimensional Morse theory,under some conditions on nonlinear term,we obt...In this paper,we are concerned with the existence of nontrivial solutions to a 2m-order nonlinear periodic boundary value problem.By the infinite dimensional Morse theory,under some conditions on nonlinear term,we obtain that there exist at least two nontrivial solutions.展开更多
文摘In this paper, the evolutionary behavior of N-solitons for a (2 + 1)-dimensional Konopelchenko-Dubrovsky equations is studied by using the Hirota bilinear method and the long wave limit method. Based on the N-soliton solution, we first study the evolution from N-soliton to T-order (T=1,2) breather wave solutions via the paired-complexification of parameters, and then we get the N-order rational solutions, M-order (M=1,2) lump solutions, and the hybrid behavior between a variety of different types of solitons combined with the parameter limit technique and the paired-complexification of parameters. Meanwhile, we also provide a large number of three-dimensional figures in order to better show the degeneration of the N-soliton and the interaction behavior between different N-solitons.
基金supported by the National Natural Science Foundation of China(10771128)Natural Science Foundation of Shanxi(2008011002-1)+2 种基金Shanxi University Science and Technology Development Project(2010110920111117)Doctorial Start-up Foundation of Datong University(2010-B-01)
文摘In this paper,we are concerned with the existence of nontrivial solutions to a 2m-order nonlinear periodic boundary value problem.By the infinite dimensional Morse theory,under some conditions on nonlinear term,we obtain that there exist at least two nontrivial solutions.
