Chirped and chirped free nonautonomous soliton solution for 4 component nonlinear Schrödinger equation in a multimode optical fiber

In this work, for the first time, analytical nonautonomous soliton solutions for a four-component coupled nonlinear Schrödinger equation with variable coefficients are constructed by means of the similarity transformation technique. A precise balance condition between the gain (loss), dispersion, and nonlinearity, which has a profound implication to control the nonautonomous soliton's dynamics, is obtained. Under this parametric condition, we study how soliton waveforms evolve with different shapes through temporally modulated group-velocity dispersion and nonlinearity parameters. We demonstrated the various rich dynamical behavior for both chirp-free and chirped solitons by a proper selection of the distributed system parameters. These results provide valuable insights into practical observation of optical solitons in real-world potential applications in the field of nonlinear fiber optics and Bose-Einstein condensates. Especially, findings are useful for the understanding of optical soliton in wavelength division multiplexing systems and inhomogeneous nonlinear optical system.