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In this article, the solitary wave and shock wave solitons for nonlinear Ostrovsky equation and Potential Kadomstev-Petviashvili equations have been obtained. The solitary wave ansatz is used to carry out the solutions.

Nonlinear wave phenomena appear in various scientific and engineering fields such as electrochemistry, electromagnetics, fluid dynamics, acoustics, cosmology, astrophysics and plasma physics. See references [

In recent time, the numerous approaches have been developed to obtain the solutions of nonlinear equations. For example the

Nonlinear wave is one of the fundamental objects of nature and a growing interest has been given to the propagation of nonlinear waves in the dynamical system. The solitary wave ansatz method [

The Ostrovsky equation is, a model of ocean currents motion, read as

where

The Potential Kadomstev-Petviashvili (PKP) equation has been considered in the following manner

In this section, the solitary wave solution or non-topological solution to the Ostrovsky Equation (1.1) and Potential Kadomstev-Petviashvili Equation (1.2) have been found using the following solitary wave ansatz. For this, we have

where

From the Equation (2.3), it can be followed

After substituting Equations (2.4)-(2.8) into (1.1), the following equation is obtained

It may be noted that

Solving the above system of equations and also set

Hence, the solitary wave solution of the OS-BBM equation is given by

It can, thus, be written from Equation (2.3) as follows

After substituting Equations (2.11)-(2.13) into Equation (1.2), the following equation is obtained

It may be noted that

Solving the above system of equations and also set

Hence, the solitary wave solution of the Potential Kadomstev-Petviashvili (PKP) equation is given by

In this section, the shock wave solution or topological solution to the Ostrovsky Equation (1.1) and Potential Kadomstev-Petviashvili Equation (1.2) have been found using the following solitary wave ansatz. For this, we can write

where

Following Equation (3.16), it can be written

After substituting Equations (3.17)-(3.20) into (1.1), the following equation is obtained

It may be noted that

Solving the above system of equations and also set

Hence, the solitary wave solution of the OS-BBM equation is given by

From Equation (3.16), it can be followed

After substituting Equations (3.22)-(3.24) into (1.2), the following equation is obtained

It may be noted that

Solving the above system of equations and also set

Hence, the solitary wave solution of the Potential Kadomstev-Petviashvili (PKP) equation is given by

The growing interest of nonlinear waves has been given to the propagation in the dynamical system. The solitary wave ansatz method is rather heuristic and processes significant features that make it practical for the determination of single soliton solutions for a wide class of nonlinear evolution equations. The solitary wave and shock wave solitons have been constructed, using the solitary wave ansatz method, for Ostrovsky equation and Potential Kadomstev-Petviashvili equation and we clearly see the consistency, which has recently been applied successfully.