Starting from an improved projective method and a linear variable separation approach, new families of variable separation solutions （including solltary wave solutlons, periodic wave solutions and rational function s...Starting from an improved projective method and a linear variable separation approach, new families of variable separation solutions （including solltary wave solutlons, periodic wave solutions and rational function solutions） with arbitrary functions [or the （2＋ 1）-dimensional general/zed Broer-Kaup （GBK） system are derived. Usually, in terms of solitary wave solutions and/or rational function solutions, one can find abundant important localized excitations. However, based on the derived periodic wave solution in this paper, we reveal some complex wave excitations in the （2＋1）-dimensional GBK system, which describe solitons moving on a periodic wave background. Some interesting evolutional properties for these solitary waves propagating on the periodic wave bactground are also briefly discussed.展开更多
基金The project supported by the Natural Science Foundation of Zhejiang Province under Grant Nos. Y604106 and Y606181, the Foundation of New Century ＂151 Talent Engineering＂ of Zhejiang Province, the Scientific Research Foundation of Key Discipline of Zhejiang Province, and the Natural Science Foundation of Zhejiang Lishui University under Grant No. KZ05005 Acknowledgments The authors are in debt to Profs. J.P. Fang, H.P. Zhu, and J.F. Zhang, and Drs. Z.Y. Ma and W.H. Huang for their fruitful discussions.
文摘Starting from an improved projective method and a linear variable separation approach, new families of variable separation solutions （including solltary wave solutlons, periodic wave solutions and rational function solutions） with arbitrary functions [or the （2＋ 1）-dimensional general/zed Broer-Kaup （GBK） system are derived. Usually, in terms of solitary wave solutions and/or rational function solutions, one can find abundant important localized excitations. However, based on the derived periodic wave solution in this paper, we reveal some complex wave excitations in the （2＋1）-dimensional GBK system, which describe solitons moving on a periodic wave background. Some interesting evolutional properties for these solitary waves propagating on the periodic wave bactground are also briefly discussed.
