In this paper, we analyze the structure of the Hardy fields associated with o-minimal expansions of the reals with exponential function. In fact, we work in the following more general setting. We take T to be the theory of a polynomially bounded o-minimal expansion P of the ordered field of real numbers. By FT we denote the set of all 0-definable functions of P . Further, we assume that T defin...

In this paper, suitable transformations and a so-called exp-function method are used to obtain different types of exact solutions for some nonlinear evolution equations with variable coefficients and nonlinear terms of any orders. The Korteweg-de Vries equation and the Burgers equation with nonlinear terms of any orders are chosen to show how to apply the exp-function method for these kinds of ...

In this paper, we analyze the structure of the Hardy fields associated with o-minimal expansions of the reals with exponential function. In fact, we work in the following more general setting. We take T to be the theory of a polynomially bounded o-minimal expansion P of the ordered field of real numbers. By FT we denote the set of all 0-definable functions of P . Further, we assume that T defin...

In this paper, a new heuristic scheme for the approximate solution of the generalized Burgers'-Fisher equation is proposed. The scheme is based on the hybridization of Exp-function method with nature inspired algorithm. The given nonlinear partial differential equation (NPDE) through substitution is converted into a nonlinear ordinary differential equation (NODE). The travelling wave solution i...

Large varieties of physical, chemical, and biological phenomena are governed by nonlinear partial differential equations. Solving nonlinear equations may guide authors to know the described process deeply and sometimes leads them to know some facts that are not simply understood through common observations. The investigation of exact solutions of nonlinear partial differential equations plays a...

The fractal derivative is adopted to describe the non-linear fractional wave equation in a space. A variational principle successfully established by semi-inverse method. two-scale method and He?s exp-function are used solve equation, good result obtained.

In this paper, we apply a relatively new technique which is called the exp-function method to construct generalized solitary and periodic solutions of Calogero-Degasperis-Fokas (CDF) equation which plays a very important role in mathematical physics, applied and engineering sciences. The suggested algorithm is quite efficient and is practically well suited for use in these problems. Numerical r...

Exact solutions of the Kawahara equation by Assas [L.M.B. Assas, J. Com. Appl. Math. 233 (2009) 97–102] are analyzed. It is shown that all solutions do not satisfy the Kawahara equation and consequently all nontrivial solutions by Assas are wrong. Recently Assas in [1] looked for exact solutions of the Kawahara equation using the Exp function method. This equation can be written as ut + α uux +...