Analytical solutions of KdV equation with relaxation effect of inhomogeneous medium

Novel curved lump and topological solitons of integrable (2+1) dimensional KMN equation

“…The equation admits special lump and topological soliton solutions that can get curved in x − y plane arbitrarily due to presence of an arbitrary function of space(x) and time(t) in their analytic expressions. Generally, solitary wave solutions with variable velocities arise in in-homogeneous media [41], in equations with variable coefficients [39,40,42]. Thus this novel bending feature is rare for an integrable equation having constant coefficients.…”