Three-Soliton Solutions

The three-soliton solutions can be obtained according to the diagram called "soliton ladder"

This solution describes a wide spectrum of the three-soliton solutions: Kink-Antikink-Kink, Antikink-Kink-Antikink, Kink-Breather and so on.

Let us demonstrate the derivation and graphical representation of the Kink-Breather collision.

Standing Kink and Moving Breather collision

The Kink-Breather collision with the Kink standing ( ) at and Breather moving with the frequency and velocity .

2D animation of the Kink-Breather interaction.

The blue line shows the Kink before the collision and the black one after the collision.

Representation of the collision with the use of 3D graphics.

The presented graphics clearly show that the standing Kink after the collision with the moving Breather do not change its shape and velocity but only shifts to a new position with coordinate . The shift can be found from the formula .

S tanding Breather and Moving Kink collision

In this section we present the interaction of standing ( ) at Breather with the Kink moving with the velocity .

2D animation of the Kink-Breather interaction.

The blue line shows the breather before the collision and the black one after the collision.

3D representation of the collision.

The presented graphics clearly show that the velocity and the oscillation frequency of the standing Breather, after the collision with the moving Kink, are unchanged. The position of the Breather shifts after collision to . The shift can be found from the formula .