Similariton regularized waves solutions of the (1+2)-dimensional non-autonomous BBME in shallow water and stability

The oscillatory motion on the ocean surface is a combination of a variety of different types of waves. The regularized waves are among them. Here, it is shown that they arise as solutions of the (1+2)-dimensional Benjamin-Bona-Mahony equation (BBME). Numerous works on (1+1)-dimensional BBME were carried in the literature. In this paper, we consider the (1+2)-dimensional non-autonomous BBME, with time -dependent coefficients. The model equation is completely new. Our objective is to find the exact solutions and investigate the relevant phenomena. To solve this issue, the extended unified method is used to find the exact solutions in the form of semi-self similar and self similar solutions. To solve this issue, simi-larity transformations are introduced. Here, the generalized unified methods (GUM) are also used in the symbolic computations. The numerical results of these solutions are evaluated and are shown graphically. Different wave patterns of regularized waves in shallow water, near ocean shores, are observed. Oscilla-tory waves and vector of lumps with troughs are shown. The time-dependent coefficients are used, here, to control the different wave patterns that take the forms of the multi-U shaped wave with basins with a trough. Further pattern formation occurs, which is in the form of two layers of lumps with troughs. Wave tunneling is also observed. These waves patterns are novel. The stability of the steady state solutions is analyzed. It is found that the stability depends significantly on the dispersion coefficient.(c) 2021 Shanghai Jiaotong University. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license ( http://creativecommons.org/licenses/by-nc-nd/4.0/ )