Exact Solution of the Sine-Gordon Equation for Multiple Collisions of Solitons

An exact solution has been obtained for the sine-Gordon equation, \(\frac{\partial^{2}\varphi}{\partial x^{2}}-\frac{\partial^{2}\varphi}{\partial t^{2}}{=}\sin\varphi\), for the case of multiple collisions of solitons with different amplitudes. It is found that solitons behave as if they were particles having apparent attractive forces between them.

Hali tarjima qilinmagan