Double-pole solitons for the higher-order matrix nonlinear Schrödinger equation: Asymptotic analysis

In the paper, we focus on the double-pole solutions and their asymptotic behavior of the higher-order matrix nonlinear Schrödinger equation. In the case of zero background conditions, we derive the double-pole solutions, which can describe degenerate solitons and illustrate their dynamic behaviors. By means of three kinds of asymptotic balances, we derive the exact Sech-type expressions for all the asymptotic soliton branches of the double-pole solutions. Through a distance expression of two asymptotic solitons, we find that the distance between two asymptotic solitons logarithmically increases with the absolute value of the coefficient of higher-order dispersion and nonlinear terms. Furthermore, we also study such physical properties of asymptotic solitons as velocity and central trajectory line, and observe that the asymptotic soliton is basically consistent with the double-pole solutions. Based on the expressions of the velocities, we show that the velocity is negatively related to the absolute value of time variable. Our results in the paper may be helpful for investigating dynamical properties and interactions of other physical systems.