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Volume 9, Number 2, 2019, Pages 568-589                                                                DOI:10.11948/2156-907X.20180103
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 differential equations, exponential rational function method, solitary wave solutions, Tzitzeica-Dodd-Bullough equation, Tzitzeica equation.
Abstract:
      The properties of Tzitzeica equations in nonlinear optics have received 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 equations type of equations, namely Tzitzeica-Dodd-Bullough and Tzitzeica equation. 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 differential equations.
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