Soliton molecules for combined mKdV-type bilinear equation  

作　　者：Zhang-Xuan Zhao Lu-Wei Zhang Wei Yang Xue-Ping Cheng 

机构地区：[1]School of Information Engineering,Zhejiang Ocean University,Zhoushan 316022,China [2]Key Laboratory of Oceanographic Big Data Mining&Application of Zhejiang Province,Zhoushan 316022,China

出　　处：《Communications in Theoretical Physics》2023年第10期1-9,共9页理论物理通讯(英文版)

基　　金：the National Natural Science Foundation of China(Grant Nos.11975204 and 12075208);the Project of Zhoushan City Science and Technology Bureau(Grant No.2021C21015);the Training Program for Leading Talents in Universities of Zhejiang Province。

摘　　要：Starting from the multi-soliton solutions obtained by the Hirota bilinear method,the soli ton molecule structures for the combined mKdV-type bilinear equation(Dt+∑n=1NαnDx2n+1)f*·f=0 are investigated using the velocity resonance mechanism.The two-soliton molecules of the mKdV-35 equation and the three-soliton molecules of the mKdV-357 equation are specifically demonstrated in this paper.With particular selections of the involved arbitrary parameters,especially the wave numbers,it is confirmed that,besides the usual multi-bright soliton molecules,the multi-dark soliton molecules and the mixed multibright-dark soliton molecules can also be obtained.In addition,we discuss the existence of the multi-soliton molecules for the combined mKdV-type bilinear equation with more higher order nonlinear terms and dispersions.The results demonstrate that when N≥4,the combined mKdVtype bilinear equation no longer admits soliton molecules comprising more than four solitons.

关 键 词：soliton molecule combined mKdV-type bilinear equation Hirota bilinear method velocity resonance mechanism 

分 类 号：O175[理学—数学]