Solitonic interactions and asymptotic analysis for a pair-transition-coupled nonlinear Schrödinger system in an isotropic optical medium

Recently, a pair-transition-coupled nonlinear Schrödinger system, which illustrates the orthogonally-polarized optical waves in an isotropic optical medium, is investigated in this paper. With respect to the slowly-varying envelopes of the two interacting optical modes, asymptotic analysis on the N solitons, double-pole solitons, triple-pole solitons and quadruple-pole solitons are processed, where N is a positive integer. For the N solitons, we obtain the expressions of the 2N line-type asymptotic solitons after some matrix operations. For the double-pole solitons, triple-pole solitons and quadruple-solitons, we obtain some curve-type asymptotic solitons resulting from the balance between the exponential and algebraic terms, and a pair of the line-type asymptotic solitons resulting from the balance between the algebraic terms. Distribution and interaction of the asymptotic solitons are shown, from which we find that the relative distances among the multi-pole solitons grow logarithmically with time. We infer that the even-pole solitons are all comprised of the curve-type asymptotic solitons, while the odd-pole solitons contain a pair of the line-type asymptotic solitons.