Abstract
In this study, a new approach that assumes and is applied to construct the traveling wave solutions of the (N + 1)-dimensional double sine-Gordon and (N + 1)-dimensional double sinh-cosh-Gordon equations. Some new elliptic integral function solutions are respectively obtained by this method, and then these solutions are converted into the Jacobi elliptic function solutions. According these results, one can easily see that this method is very effective mathematical tool for the (N+1)-dimensional nonlinear physical problems.
Highlights
The nonlinear evolution equations have become of ever greater interest in the modelling of real life problems
The investigation of various traveling wave solutions to (N+1)-dimensional double sine-Gordon and (N+1)dimensional double sinh-cosh-Gordon equations have been widely studied by many authors [7,8,9]
Some new Jacobi elliptic function solutions are obtained by the using of this method
Summary
The nonlinear evolution equations have become of ever greater interest in the modelling of real life problems. The investigation of various traveling wave solutions to (N+1)-dimensional double sine-Gordon and (N+1)dimensional double sinh-cosh-Gordon equations have been widely studied by many authors [7,8,9]. A variety of effective methods have been defined to construct the traveling wave solutions of nonlinear partial differential equations. It is given the new function method as one of most important methods and its applications [1014]. We apply the new function method, based on sine, sinh functions, to (N+1)-dimensional double sine-Gordon and (N+1)-dimensional double sinh-cosh-Gordon equations. The obtained results reveal that the new function method is powerful mathematical tool for solving the (N+1)-dimensional sine-Gordon and sinhcosh-Gordon equations
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