Analytical and Multishaped Solitary Wave Solutions for Extended Reduced Ostrovsky Equation

Abstract

We present the analytical and multishaped solitary wave solutions for extended reduced Ostrovsky equation (EX-ROE). The exact solitary (traveling) wave solutions are expressed by three types of functions which are hyperbolic function solution, trigonometric function solution, and rational solution. These results generalized the previous results. Multishape solitary wave solutions such as loop-shaped, cusp-shaped, and hump-shaped can be obtained as well when the special values of the parameters are taken. The (/)-expansion method presents a wide applicability for handling nonlinear partial differential equations.

A New Integro-Differential Equation for Rossby Solitary Waves with Topography Effect in Deep Rotational Fluids

“…More problems on KdV-BO-Burgers equation such as the analytical solutions, integrability, and infinite conservation quantities are not studied in the paper due to limited space. In fact, there are many methods carried out to solve some equations with special nonhomogenous terms [28] as well as multiwave solutions and other form solution [29,30] of homogenous equation. These researches have important value for understanding and realizing the physical phenomenon described by the equation and deserve to carry out in the future.…”

Traveling Wave Solutions of Two Nonlinear Wave Equations by (G′/G)-Expansion Method

“…By substituting (27) and (28) into (25) and collecting all terms with the same power of / together, the left-hand sides of (25) are converted into the polynomials in / . Equating the coefficients of the polynomials to zero yields a set of simultaneous algebraic equations for 0 , 1 , , , 1 , 2 and as follows:…”

“…Recently, Wang et al [26] introduced a new approach, namely, the ( / )-expansion method, for a reliable treatment of the nonlinear wave equations. The useful ( / )-expansion method is then widely used by many authors [27][28][29][30].…”