A governing equation of Rossby waves and its dynamics evolution by Bilinear neural network method

Abstract

This paper studies an extended evolution equation of large-scale waves by means of bilinear neural network method, which is obtained from local Cartesian coordinate system of the basic equation set by using scaling analysis method and perturbation expansions method. First, we convert the equation into a Hirota equation by using variable transformation. Then, we give the structure framework and the model of the bilinear neural network. We build the test function in two dimensions: depth and breadth. With choosing appropriate activation functions and neuron coefficients, we get many rational function exact solutions, including rogue waves and interaction phenomenon consisting of rogue wave and soliton wave. At last, the figures of these exact solutions are exhibited by selecting suitable value of parameters. We think that these results are very important in ocean dynamics.

Higher rogue and rogue-soliton interaction solutions of a (2 + 1) dimensional nonlinear model in fluid mechanics

“…where t = + ax by, and g > 0 1 is a constant. Substituting (10) into (9), we get an equation group and pick a set of the solutions to continue analysis, substituting (11) into (10), then into (8), we can get the second order rogue wave where H satisfies (10) and (11).…”

“…Rogue waves are unexpected large water waves that appear and disappear suddenly, with extremely steep peaks, and even pose a great threat to large ships [1][2][3][4][5][6][7]. Interaction solutions can be used to explain nonlinear phenomena, especially in climate modeling and prediction, weather forecasting, fluid dynamics, geophysics, etc Many scholars did a lot of work on the interaction phenomena and obtained many meaningful interaction solutions [8][9][10][11][12][13][14][15]. It is a hot research topic about the interaction between rogue wave and other nonlinear waves.…”