Derivation and Multisoliton Solutions of the High‐Order Fractional Nonlinear SchröDinger Equation for the Rossby Waves

ABSTRACT Fractional models are generally more adept at providing a detailed description of the dynamic behavior in complex oceanic systems. In this paper, starting from the fractional barotropic nondivergent vorticity equation, a high‐order fractional nonlinear Schrödinger equation is derived to describe the evolution of Rossby waves in fractal. The derivation method in this paper differs from traditional approaches used for fractional equations, resulting in a more concise process. To study the solutions of the equation, we apply the Darboux transformation method and obtain the fractional multisoliton solutions for the equation. Then we create visual representations of the fractional soliton solutions and discuss the impact of fractional coefficients on the amplitude and wave width of Rossby waves.