Application of exp ) ) ( (-expansion method to find the exact solutions of Shorma-Tasso-Olver Equation

In this work, we present traveling wave solutions for the Shorma-Tasso-Olver equation. The idea of exp )) ( (    expansion method is used to obtain exact solutions of that equation. The traveling wave solutions are expressed by the exponential functions, the hyperbolic functions, the trigonometric functions solutions and the rational functions. It is shown that the method is awfully effective and can be used for many other nonlinear evolution equations (NLEEs) in mathematical science and engineering.


INTRODUCTION
The study of nonlinear evolution equation (NLEE) has much remarkable progress in the past few decades.Most of the phenomena in real world can be described using non-linear equations.A nonlinear phenomenon plays a vital role in applied mathematics, physics and engineering branches.Most of the complex nonlinear equations in plasma physics, fluid dynamics, chemistry, biology, mechanics, elastic media and optical fibers etc., can be explained by nonlinear evolution equations.There are a lot of NLEEs that are integrated using various mathematical techniques.
Recently, Wang and Xu (2013a,b) and Wang et al. (2014), presented some exact solutions of different nonlinear evolution equations by Lie group analysis.Wang and Xu (2013a) established exact solutions of nonlinear time fractional Sharma-Tasso-Olver equation via Lie group analysis.Zhao and Li (2013)

METHODOLOGY
In this section we describe exp )) ( (    -expansion method for finding traveling wave solutions of nonlinear evolution equations (Miura, 1978).Suppose that a nonlinear equation, say in two independent variables x and t is given by: 0 .........) ,......... , , , , , (  and its partial derivatives in which the highest order derivatives and nonlinear terms are involved.In the following, we give the main steps of this method: Step 1 Combining the independent variables x and t into one The travelling wave transformation Equation ( 2  and so on.
Step 2 We suppose that Equation (3) has the formal solution: Equation ( 5) gives the following solutions: When , the positive integer n can be determined by considering the homogeneous balance between the highest order derivatives and the nonlinear terms appearing in Equation (3).
Step 3 We substitute Equation (4) into Equation ( 3) and then we account the function

Application of the method
Here we will present the )) ( exp(    expansion method to construct the exact solutions and then the solitary wave solutions of the Shorma-Tasso-Olver equation.First consider the Shorma-Tasso-Olver equation in the forms: Using the wave transformation Equation ( 12) is integrable, therefore, integrating with respect to  once yields: Now, balancing the highest order derivative Solving the Equation (15) -Equation ( 18), yields: Now substituting Equation ( 6) -Equation (10) into Equation ( 19) respectively, we get the following five traveling wave solutions of modified equal width equation.
For Case 2: Now substituting the values of Now substituting Equation (6) -Equation (10) into Equation ( 20) respectively, we get the following five traveling wave solutions of modified equal width equation.

GRAPHICAL REPRESENTATION
The graphical demonstrations of obtained solutions for particular values of the arbitrary constants are shown in Figure 1 to 5 with the aid of commercial software Maple 13.

Conclusion
In this paper, we have applied the  Singular Kink of the exact solutions of NLEEs.Also, we observe that this method can be also applied to other nonlinear evolution equations.
along with general solutions of Equation (5) completes the determination of the solution of Equation (1).

,
E is an arbitrary constant.
the exact solution of the Shorma-Tasso-Olver equation and constructed some new exact travelling wave solutions.The travelling wave solutions expressed by the hyperbolic functions, the trigonometric functions solutions and the rational functions.This paper shows that the is quite efficient and effective to find Figure Figure 4. Singular kink of