A new dynamic model of ocean internal solitary waves and the properties of its solutions

摘要

In this paper, considering the frictional dissipation, we use the multi-scale analysis and perturbation methods to obtain a new model: the (2 + 1)-dimensional modified Kadomtsev-Patviashvili-Benjamin-Ono-Burgers (mKP-BO-Burgers) equation, to describe internal solitary waves in the ocean. Compared with the traditional BO model, the mKP-BO-Burgers model takes account of frictional dissipation, and its nonlinearity is stronger. Next, in order to better understand the characteristics of internal solitary waves, the integer order mKP-BO-Burgers equation is converted into the time-fractional form by using semi inverse and Agrawal's methods. And then, conservation laws of the time-fractional mKP-BO-Burgers equation are derived. The results show that when the dissipation disappears, the mass, momentum and energy are conserved. Finally, we obtain the N-soliton solutions of the new model, analyze the asymptotic behaviors of the N-soliton solutions, discuss the interaction between the two solitons, and get some conclusions. (C) 2020 Elsevier B.V. All rights reserved.