Solutions of sine Gordon equation by generalized exponential function methods
Keywords:
Sine Gordon equations, exp-function methods, multiwave solutionsAbstract
The sine Gordon equation (sG) is hyperbolic partial differential equation involving the d’Alembert operator and the sine of the unknown function. The importance of the equation grew from 1970, when led to kink and antikink solitons discovery. In the development of soliton theory, the multiwave solutions have gradually become a field of study of nonlinear science. Such multiwave solutions can be obtained by the exp function method proposed by He and Wu in 2006, the method is used in solving different classes of nonlinear differential equations such as KdV, mKdV and sGs. In this paper we describe the exp-function method in the solution of the sG equation, the results presented are for soliton solutions for single, two and three wave. We chose the positive sign in the solution and found that for negative values Z the amplitude of the solution is close to zero, while for positive values Z it is close to 2pi.
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