In this paper, the hyperbolic tangent function (tanh) method is used in finding soliton solutions of Generalized Fisher Equation (GFE) and Spalding Equation (SE). It is shown that the tanh method provides a straight forward and powerful tool for solving Nonlinear Evolution Equations (NLEEs) in Mathematical Physics.

In recent years, nonlinear phenomena play a crucial role in appliedmathematics and physics. Directly searching for exact solutions of nonlinear partial differential equations (PDEs) has become more and more attractive partly due to the availability of computer symbolic systems like Mathematica or Maple that allow us to perform some complicated and tedious algebraic calculation on a computer as ...

Nonlinear evolution equations have a major role in various scientific and engineering fields, such as fluid mechanics, plasma physics, optical fibers, solid state physics, chemical kinematics, chemical physics and geochemistry. Nonlinear wave phenomena of dispersion, dissipation, diffusion, reaction and convection are very important in nonlinear wave equations. In recent years, quite a few meth...

Abstract In this paper, other types of exact solution of a first-order nonlinear ordinary differential equation is further investigated. By using the solutions of this equation, and a new general ansatz, we give some types of solutions of a class of nonlinear partial differential equations and MKdV equation. These solutions includes solitary wave solutions, singulary solitary solitary solutions...

In this paper we further improve the modified extended tanh-function method to obtain new exact solutions for nonlinear partial differential equations. Numerical applications of the proposed method are verified by solving the improved Boussinesq equation and the system of variant Boussinesq equations. The new exact solutions for these equations include Jacobi elliptic doubly periodic type, Weie...

Foaming occurs in many distillation and absorption processes. The drainage of liquid foams involves the interplay of gravity, surface tension, and viscous forces. In this paper, we use a semi analytic method, the Adomian decomposition method, and an analytic method, the tanh method to handle the foam drainage equation. The powerful tanh method gives the solution in a closed form. However, Adomi...

in this paper, we have studied on the solutions of modied kdv equation andalso on the stability of them. we use the tanh method for this investigationand given solutions are good-behavior. the solution is shock wave and can beused in the physical investigations

The modified tanh-coth function method is used to obtain new exact travelling wave solutions for Zhiber-Shabat equation and the related equations: Liouville equation, sinh-Gordon equation, Dodd-Bullough-Mikhailov equation, and Tzitzeica-Dodd-Bullough equation. Exact travelling wave solutions for each equation are derived and expressed in terms of hyperbolic functions, trigonometric functions an...

The Mathematica implementation of the tanh and sech-methods for computing exact travelling wave solutions of nonlinear partial differential equations (PDEs) is presented. These methods also apply to ordinary differential equations (ODEs). New algorithms are given to compute polynomial solutions of ODEs and PDEs in terms of the Jacobi elliptic functions. An adaptation of the tanh-method to nonli...