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 ...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.展开更多
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。
文摘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.
