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SOLITARY WAVE SOLUTIONS TO THE TZITZEICA TYPE EQUATIONS OBTAINED BY A NEW EFFICIENT APPROACH
Behzad Ghanbari,Mustafa Inc,Lavdie Rada
Keywords:Symbolic computations, Nonlinear partial di erential equations, Exponential rational function method, Solitary wave solutions, Tzitzeica-Dodd- Bullough equation, Tzitzeica equation.
Abstract:
      The properties of Tzitzeica equations in nonlinear optics have re- ceived a great attention of many recent studies. In this work, the so-called generalized exponential rational function method (GERFM) has been applied for finding the analytical solution of two nonlinear partial differential equa- tions type of equations, namely Tzitzeica-Dodd-Bullough and Tzitzeica equa- tion. The proposed method provides a wide range of closed-form travelling solutions leading to a very effective and simply-applied method by means of a symbolic computation system. The method not only provides a general form of solutions with some free parameters but also shows potential application to other types of nonlinear partial di erential equations.