Soliton molecules and asymmetric solitons in fluid systems via velocity resonance

Abstract

Soliton molecules may be formed in some possible mechanisms in both theoretical and experimental aspects. In this letter, we introduce a new possible mechanism, the velocity resonant, to form soliton molecules. Under the resonant mechanism, two solitons may be formed to a kink-antikink molecule, an asymmetric soliton, a two-peak soliton and/or a far away bounded molecule depended on the selections of the wave numbers and the distance between two solitons of the molecule. The results are exhibited via three well known fifth order integrable systems which approximately solve a general fluid model that also appeared in many other physical fields. The interactions among multiple soliton molecules for these three integrable systems are elastic.

Figures (8)

• Figure 1: Density plot of the soliton molecule for the SK system described by Eq. (\ref{['2sol']}) with the parameter selections \ref{['skm1']}.
• Figure 2: Soliton molecule structure for the fifth order KdV system described by Eq. (\ref{['2sol']}) with the parameter selections \ref{['skm1']}.
• Figure 3: Asymmetric soliton for the fifth order KdV equation described by Eq. (\ref{['2sol']}) with the parameter selections \ref{['pFig3']}.
• Figure 4: Asymmetric soliton for the SK system described by Eq. (\ref{['2sol']}) with the same parameter selections as in Fig. 3 except for $\xi_{20}=0.1$.
• Figure 5: Plot of the elastic interaction property between two soliton molecules for the fifth order KdV equation described by \ref{['NS']} with $N=4,\ \alpha=3, \ \beta=\beta_1=1$ and the parameter selections \ref{['2mol']}.