The N-soliton molecule for the combined (2N+1)th-order Lax’s KdV equation

Abstract

Using the Hirota’s bilinear method combined with the velocity resonance mechanism, the two-soliton molecule, the three-soliton molecule and the four-soliton molecule for the third-fifth-order Lax’s KdV equation, the third-fifth-seventh-order Lax’s KdV equation and the third-fifth-seventh-ninth-order Lax’s KdV equation are obtained respectively. To show the dynamical properties of these soliton molecules, their three dimensional profiles and the density plots with particular choices of the involved free parameters are well displayed. More generally, by summarizing the three expressions for soliton molecules, the general formula of N-soliton molecule for combined (2N+1)th-order Lax’s KdV equation are well given.

Keywords

• Soliton molecule
• Combined (2N+1)th-order Lax’s KdV equation
• Velocity resonance mechanism
• Hirota’s bilinear method