Related papers: (G'/G)-Expansion Method and Weierstrass Elliptic F…
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.
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…
This paper presents two new Weierstrass elliptic function solutions of the projective Riccati equations and four conversion formulas for converting the Weierstrass elliptic functions to the hyperbolic and trigonometric functions. The…
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…
In this work, we apply the (1/G')-expansion method to produce the novel soliton solution of the Gilson-Pickering equation. This method is fundamental on homogeneous balance procedure that gives the order of the estimating polynomial-type…
A Weierstrass type projective Riccati equation expansion method is proposed by using the Weierstrass elliptic function solutions of the projective Riccati equations and the conversion formulas which transform the Weierstrass elliptic…
The nonlinear wave solutions to coupled mKdV equations with variable coefficients are obtained by using the F-expansion method, including 12 kinds of Jacobi elliptic function solutions. In the limit cases, the torsional wave solutions,…
In this work an extended elliptic function method is proposed and applied to the generalized shallow water wave equation. We systematically investigate to classify new exact travelling wave solutions expressible in terms of quasi-periodic…
New problem is studied that is to find nonlinear differential equations with special solutions expressed via the Weierstrass function. Method is discussed to construct nonlinear ordinary differential equations with exact solutions. Main…
This paper is dedicated to finding the solutions of the equation of the loaded modified Korteweg-de Vries. By the way, it is shown to find the solutions via $(G'/G)$-expansion method that is one of the most effective ways of finding…
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…
A review of three-dimensional waves on deep-water is presented. Three forms of three dimensionality, namely oblique, forced and spontaneous type, are identified. An alternative formulation for these three-dimensional waves is given through…
A new algebraic method to find two special types of exact traveling wave solutions and the solitary type solutions to some conformable fractional partial differential equations is proposed. The two special types of solutions given by the…
Exact bright, dark, antikink solitary waves and Jacobi elliptic function solutions of the generalized Benjamin-Bona-Mahony equation with arbitrary power-law nonlinearity will be constructed in this work. The method used to carry out the…
The variable separated ODE method is extended by choosing the additional variable separated equation as the general elliptic equation. More exact traveling wave solutions of nonlinear equations are obtained by using the method of comparison…
We consider an extension of the methodology of the modified method of simplest equation to the case of use of two simplest equations. The extended methodology is applied for obtaining exact solutions of model nonlinear partial differential…
In this article, we present a comprehensive analytical study to obtain the exact traveling wave solutions to a new formed model of the (2+1)-dimensional BKP equation. We construct exact solutions of the considered model using a recently…
We study a family of separable potentials with and without added contact interactions by solving the associated Lippmann-Schwinger equation with two coupled partial waves. The matching of the resulting amplitude matrix with the…
The paper is devoted to analysis of different models that describe waves in fluid-filled and gas-filled elastic tubes and development of methods of calculation and numerical analysis of solutions with solitary waves and kinks for these…
The one-dimensional Ginzburg-Landau (GL) Equation is considered. We use the recently developed extended F-expansion method to obtain spiral wave solution of one-dimensional GL Equation.