Dynamics of the smooth positons of the coupled nonlinear Schrödinger equations

Abstract

In this paper, we formulate the compact determinant representation formula of n-soliton solution for the coupled nonlinear Schrödinger equations (CNLS) equations, and obtain the expression of the n-positon solutions by using the Taylor expansion to degenerate eigenvalues λ3j−2→λ1(j=1,2,…,n). Especially, the expressions of two-positon and three-positon solutions are obtained by the corresponding formulas. Furthermore, the dynamical properties of the smooth positons of the CNLS equations are analyzed by using the method of decomposition of the modulus square, which can be used to approximately describe the trajectories and time-dependent ‘phase shifts’ of positons after the collision. In addition, the collision between soliton and positon, and mutual collision of two two-positons are graphically discussed, and these collision properties are remarkably different from before.