New Solitary Wave and Multiple Soliton Solutions for the Time-Space Coupled Fractional mKdV System with Time-Dependent Coefficients

In this paper, a simplified bilinear method combined with a fractional transform has been used to obtain new multiple soliton solutions for the Fractional coupled modified KdV systems with variable coefficients. These systems are a generalized model in plasma physics, ocean dynamics and in nonlinear lattice. Realistic N-soliton solutions are obtained for the above fractional system and we developed tools which allow analyzing and controlling the dynamical behaviors of such solutions. To the best of our knowledge, the obtained analytic multi-soliton solutions we have derived are new.