N-Soliton Solution of the K-dV Equation with Loss and Nonuniformity Terms

Abstract

N -soliton solution of the Korteweg-de Vries equation with loss and nonuniformity terms \begin{aligned} u_{t}+2{\alpha}u+(C_{0}+{\alpha}x)u_{x}+6uu_{x}+u_{xxx}=0, \end{aligned} are obtained. The solutions express multisolitons damping in time without radiation and mutually colliding in nonuniform media with a relaxation effect.