Exact Multisoliton Solutions of the Self-Induced Transparency and Sine-Gordon Equations

Abstract

We confirm that the previously conjectured $N$-soliton solution of the self-induced-transparency equations is a solution for all $N$. The solution is transformed to give an exact solution of the since-Gordon equation describing multiple collision of $N$ kinks with different velocities. Simple asymptotic forms of both solutions are given.