Double Wronskian Solutions for a Generalized Nonautonomous Nonlinear Equation in a Nonlinear Inhomogeneous Fiber**Supported by the Fundamental Research Funds for the Central Universities under Grant No. 2018MS132

Abstract

A generalized nonautonomous nonlinear equation, which describes the ultrashort optical pulse propagating in a nonlinear inhomogeneous fiber, is investigated. N-soliton solutions for such an equation are constructed and verified with the Wronskian technique. Collisions among the three solitons are discussed and illustrated, and effects of the coefficients σ1(x, t), σ2(x, t), σ3(x,t) and v(x, t) on the collisions are graphically analyzed, where σ1(x, t), σ2(x, t), σ3(x, t) and v(x, t) are the first-, second-, third-order dispersion parameters and an inhomogeneous parameter related to the phase modulation and gain(loss), respectively. The head-on collisions among the three solitons are observed, where the collisions are elastc. When σ1(x, t) is chosen as the function of x, amplitudes of the solitons do not alter, but the speed of one of the solitons changes. σ2(x, t) is found to affect the amplitudes and speeds of the two of the solitons. It reveals that the collision features of the solitons alter with σ3(x, t) = −1.8x. Additionally, traveling directions of the three solitons are observed to be parallel when we change the value of v(x, t).