Abstract
Abstract
Starting from the multi-soliton solutions obtained by the Hirota bilinear method, the soliton molecule structures for the combined mKdV-type bilinear equation
(
D
t
+
∑
n
=
1
N
α
n
D
x
2
n
+
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 multi-bright-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 mKdV-type bilinear equation no longer admits soliton molecules comprising more than four solitons.
Funder
National Natural Science Foundation of China
Subject
Physics and Astronomy (miscellaneous)