Resumen de Mixed Higher-Order Rogue Waves and Solitons for the Coupled Modified Nonlinear Schrödinger Equation

Tao Xu, Guoliang He, Ming Wang, Yanqing Wang

• The coupled modified nonlinear Schrödinger equation, which appears in birefringent optical fibers and describes the propagation of the short pluses in picosecond or femtosecond regions, is researched by the Darboux transformation. Utilizing both the Darboux transformation and the received special vector solution of the Lax pair, the general solutions for the coupled modified nonlinear Schrödinger equation are generated. Through searching the double-root condition of the spectral characteristic equation for the matrix in the Lax pair, we can obtain the reduced solutions that mixed higher-order rogue waves and solitons. Besides, the reduced solutions are mainly discussed in the following two types: (1) one component includes higher-order rogue waves and multi-bright-solitons, the other one is higher-order rogue waves and multidark-solitons; (2) higher-order rogue waves as the degenerate case. The dynamical behaviors of these reduced solutions are detailedly discussed.