A numerical study of the diverging probability density function of flat-top solitons in an extended Korteweg–de Vries equation

Abstract

We consider an extended Korteweg–de Vries (eKdV) equation, the usual Korteweg–de Vries equation with inclusion of an additional cubic nonlinearity. We investigate the statistical behavior of flat-top solitary waves described by an eKdV equation in the presence of weak dissipative disorder in the linear growth/damping term. With the weak disorder in the system, the amplitude of solitary wave randomly fluctuates during evolution. We demonstrate numerically that the probability density function of a solitary wave parameter κ which characterizes the soliton amplitude exhibits loglognormal divergence near the maximum possible κ value.