Related papers: Solitary wave solutions of several nonlinear PDEs …
We study traveling wave solutions of an equation for surface waves of moderate amplitude arising as a shallow water approximation of the Euler equations for inviscid, incompressible and homogenous fluids. We obtain solitary waves of…
The modified method of simplest equation is applied to the extended Korteweg - de Vries equation and to generalized Camassa - Holm equation. Exact traveling wave solutions of these two nonlinear partial differential equations are obtained.…
We discuss the application of a variant of the method of simplest equation for obtaining exact traveling wave solutions of a class of nonlinear partial differential equations containing polynomial nonlinearities. As simplest equation we use…
The method of simplest equation is applied for obtaining exact solitary traveling-wave solutions of nonlinear partial differential equations that contain monomials of odd and even grade with respect to participating derivatives. The used…
We apply the method of simplest equation for obtaining exact solitary traveling-wave solutions of nonlinear partial differential equations that contain monomials of odd and even grade with respect to participating derivatives. We consider…
In this paper we employ three recent analytical approaches to investigate the possible classes of traveling wave solutions of some members of a family of so-called short-pulse equations (SPE). A recent, novel application of phase-plane…
We present a short review of the evolution of the methodology of the Method of simplest equation for obtaining exact particular solutions of nonlinear partial differential equations (NPDEs) and the recent extension of a version of this…
We propose a simple algebraic method for generating classes of traveling wave solutions for a variety of partial differential equations of current interest in nonlinear science. This procedure applies equally well to equations which may or…
In the present work, we revisit the so-called regularized short pulse equation (RSPE) and, in particular, explore the traveling wave solutions of this model. We theoretically analyze and numerically evolve two sets of such solutions. First,…
Our goal is to find closed form analytic expressions for the solitary waves of nonlinear nonintegrable partial differential equations. The suitable methods, which can only be nonperturbative, are classified in two classes. In the first…
We present an elementary method to obtain the equations of the shallow-water solitary waves in different orders of approximation. The first two of these equations are solved to get the shapes and propagation velocities of the corresponding…
In this work, we study the generalized shallow water wave equation to obtain novel solitary wave solutions. The application of this non-linear model can be found in tidal waves, weather simulations, tsunami prediction, river and irrigation…
In this article, we follow an idea that is opposite to the idea of Hopf and Cole: we use transformations in order to transform simpler linear or nonlinear differential equations (with known solutions) to more complicated nonlinear…
The modification of simplest equation method to look for exact solutions of nonlinear partial differential equations is presented. Using this method we obtain exact solutions of generalized Korteweg-de Vries equation with cubic source and…
Some effects of surface tension on fully-nonlinear, long, surface water waves are studied by numerical means. The differences between various solitary waves and their interactions in subcritical and supercritical surface tension regimes are…
A forced KdV equation is derived to describe weakly nonlinear, shallow water surface wave propagation over non trivial bottom boundary condition. We show that different functional forms of bottom boundary conditions self-consistently…
Traveling wave solutions to Kawahara equation (KE), transmission line (TL), and Korteweg-de Vries (KdV) equation are found by using an elliptic function method which is more general than the $\mathrm{tanh}$-method. The method works by…
wave solutions to nonlinear partial differential equations. We simplify the so called (G'/G)-expansion method and apply two of those methods to simple physical problems.
New method is presented to look for exact solutions of nonlinear differential equations. Two basic ideas are at the heart of our approach. One of them is to use the general solutions of the simplest nonlinear differential equations. Another…
Direct algebraic method of obtaining exact solutions to nonlinear PDE's is applied to certain set of nonlinear nonlocal evolutionary equations, including nonlinear telegraph equation, hyperbolic generalization of Burgers equation and some…