Pseudospectral method is an alternative of finite differences and finite elements method to solve nonlinear partial differential equations (PDEs), especially in nonlinear waves. The Pseudospectal method is very efficient because it use the fast fourier transform to calculate discrete Fourier transform in the algorithm. In this paper, the Pseudospectral scheme is modified by adding the linear damping effect and de-aliasing technique, and has been tested in Ostrovsky equation, where Ostrovsky equation is a modified of Korteweg-de Vries equation with an addition of background Earth’s rotation. The addition of the linear damping is to prevent the possibility of radiated waves re-entering from the boundaries and disturbing the main wave structure. Most of the numerical simulations occur with the aliasing errors due to pollution of numerically calculated Fourier transform by higher frequencies component because of the truncation of the series. To prevent this, the de-aliasing technique is implemented on the nonlinear term and linear damping region by setting of the amplitudes to be zero at the end of both boundaries. Therefore, the simulation results of Pseudospectral method will be smooth without any high frequency errors even for the high amplitude of the waves from initial condition.

A nonlinear equation of the Korteweg–de Vries equation usually describes internal solitary waves in the coastal ocean that lead to an exact solitary wave solution. However, in any real application, there exists the Earth’s rotation. Thus, an additional term is required, and consequently, the Ostrovsky equation is developed. This additional term is believed to destroy the solitary wave solution and form a nonlinear envelope wave packet instead. In addition, an internal solitary wave is commonly disseminated over the variable topography in the ocean. Because of these effects, the Ostrovsky equation is retrieved by a variable-coefficient Ostrovsky equation. In this study, the combined effects of both background rotation and variable topography on a solitary wave in a two-layer fluid is studied since internal waves typically happen here. A numerical simulation for the variable-coefficient Ostrovsky equation with a variable topography is presented. Two basic examples of the depth profile are considered in detail and sustained by numerical results. The first one is the constant-slope bottom, and the second one is the specific bottom profile following the previous studies. These indicate that the combination of variable topography and rotation induces a secondary trailing wave packet.