Derivation and rogue waves of the fractional nonlinear Schrödinger equation for the Rossby waves

Abstract

The Cartesian coordinate system is not sufficient to study wave propagation on the coastline or in the sea where the terrain is extremely complicated, so it is necessary to study it in an unconventional coordinate system, fractals. In this paper, from the governing equations of fluid, the fractional nonlinear Schrödinger equation is derived to describe the evolution of Rossby waves in fractal by using multi-scale analysis and perturbation method. Based on the equation, the rogue-wave solution is obtained by the integral preserving transformation to explain some serious threats at sea.