Soliton molecules and abundant interaction solutions of a general high-order Burgers equation

Abstract

In this work, many kinds of resonant excitations to the N-solitary waves solution are constructed for a (1+1)-dimensional general high-order Burgers (HB) equation. And the complexiton solution, half periodic kink (HPK) and soliton molecules of the (1+1)-dimensional HB equation are found. In particular, for a fourth-order Burgers equation, the explicit expressions and forming conditions for the soliton molecule and HPK are revealed. The three-soliton molecule, two-soliton molecule and HPK molecule are also proposed and depicted. The soliton molecule-kink type and HPK molecule-kink type interaction solutions can exhibit abundant fusion and fission phenomena.

Keywords

• Interaction solution
• Soliton molecule
• Burgers equation
• Half periodic kink