Dodd Bullough Mikhailov Research Articles

New type soliton solutions for the Zhiber–Shabat and related equations

In this paper, ansatz approach with the Jacobi elliptic functions is used to construct the solutions for the Zhiber–Shabat and related equation: Liouville equation, Dodd–Bullough–Mikhailov (DBM) equation, sinh–Gordon equation, and Tzitzeica–Dodd–Bullough (TDB) equation. Cnoidal, snoidal, triangular and periodic wave solutions for these equations are obtained. The constraint relations between the model coefficients and the damping coefficient for existence of soliton solutions are derived. The remarkable properties of the obtained solutions are showed in four interesting figures.

G'/G-Expansion method for related equations to the Zhiber–Shabat equation

In this work G'/G-expansion method has been employed for related equations to ZhiberShabat equation: Liouville equation, sinh-Gordon equation, DoddBulloughMikhailov (DBM) equation. It is shown that G'/G- expansion method provides a very effective and a powerful mathematical tool, for solving these equations.

Exact travelling solutions for some nonlinear physical models by ( G′/ G)-expansion method

In this paper, we establish exact solutions for some special nonlinear partial differential equations. The (G′/G)-expansion method is used to construct travelling wave solutions of the two-dimensional sine-Gordon equation, Dodd–Bullough–Mikhailov and Schrodinger–KdV equations, which appear in many fields such as, solid-state physics, nonlinear optics, fluid dynamics, fluid flow, quantum field theory, electromagnetic waves and so on. In this method we take the advantage of general solutions of second-order linear ordinary differential equation (LODE) to solve many nonlinear evolution equations effectively. The (G′/G)-expansion method is direct, concise and elementary and can be used with a wider applicability for handling many nonlinear wave equations.

Application of the ( [formula omitted])-expansion method for the Zhiber–Shabat equation and other related equations

In this paper, the exact traveling wave solutions of the Zhiber–Shabat equation and the related equations: Liouville equation, Dodd–Bullough–Mikhailov (DBM) equation, sinh–Gordon equation, and Tzitzeica–Dodd–Bullough (TDB) equation are studied by using the ( G ′ G )-expansion method. Solitons and periodic solutions for these equations are formally derived.

The [formula omitted]-expansion method for Tzitzéica type nonlinear evolution equations

In this work, the ( G ′ G ) -expansion method is applied for constructing more general exact solutions of the three nonlinear evolution equations with physical interest namely, the Tzitzéica equation, the Dodd–Bullough–Mikhailov (DBM) equation and the Tzitzéica–Dodd–Bullough (TDB) equation. Our work is motivated by the fact that the ( G ′ G ) -expansion method provides not only more general forms of solutions but also periodic and solitary waves. If we set the parameters in the obtained wider set of solutions as special values, then some previously known solutions can be recovered. The method appears to be easier and faster by means of a symbolic computation system.

Exact travelling wave solutions of some nonlinear equations by [formula omitted]-expansion method

Here we find exact solutions of some nonlinear evolution equations within the framework of the G ′ G -expansion method. Exact solutions of five nonlinear equations of physical importance viz. the coupled Schrodinger–KdV equation, the coupled nonlinear Reaction–Diffusion equation, the Foam Drainage equation, the Phi-Four equation and the Dodd–Bullough–Mikhailov equation are obtained. These general solutions can be reduced in some standard results derived by some other methods. Two and three dimensional plots of some of the results are also presented.

The tanh method for travelling wave solutions to the Zhiber–Shabat equation and other related equations

The tanh method and the extended tanh method are used for handling the Zhiber–Shabat equation and the related equations: Liouville equation, sinh-Gordon equation, Dodd–Bullough–Mikhailov (DBM) equation, and Tzitzeica–Dodd–Bullough equation. Travelling wave solutions of different physical structures are formally derived for each equation.

Exp-function method for nonlinear wave equations

Abstract In this paper, a new method, called Exp-function method, is proposed to seek solitary solutions, periodic solutions and compacton-like solutions of nonlinear differential equations. The modified KdV equation and Dodd–Bullough–Mikhailov equation are chosen to illustrate the effectiveness and convenience of the suggested method.

The tanh method: solitons and periodic solutions for the Dodd–Bullough–Mikhailov and the Tzitzeica–Dodd–Bullough equations

Abstract The tan h method is applied to the Dodd–Bullough–Mikhailov and the Tzitzeica–Dodd–Bullough equations. Solitons and periodic solutions for these equations are formally derived. The Painleve property v = e ± u will be employed to back up our analysis and to emphasize the effectiveness of the presented method.

Applications of extended tanh method to ‘special’ types of nonlinear equations

In this paper, we explore more applications of extended tanh method to some special nonlinear equations. Such equations are not of differential polynomial form so that cannot be directly dealt with by tanh method or extended tanh method. As examples, we apply a recently proposed extended tanh method to build some new explicit solutions for (2+1)-dimensional sine-Gordon equation, Dodd–Bullough–Mikhailov equation and coupled Schrödinger-KdV equation.

Chelates of o-quinone—with Cu(II) and Fe(III) acting as hydroxylators and oxidators. Organic catalysts: Catalytic activity of o-quinones

In this article, we shall introduce a new and more general traveling wave solutions for Dodd–Bullough–Mikhailov equation and coupled Higgs equation according to the modified extended tanh-function method with the aid of Maple 16. The important fact of this method is to explain the solitary wave solutions for nonlinear partial differential equations (NLPDEs.) which illustrate the physical phenomena and help other researchers for investigating the stability of Dodd–Bullough–Mikhailov equation and coupled Higgs equation. The traveling wave solutions; solitary wave solutions; dark and bell soliton solutions of nonlinear Dodd–Bullough–Mikhailov and coupled Higgs dynamical equations are constructed by employing modified extended tanh method, which have important applications in applied mathematics and physics. Furthermore, we also present the formation conditions of the traveling wave solutions; solitary wave solutions; dark and bell soliton solutions for these equations. Comparison between our results and the well-known results will be presented.