New extended direct algebraic method for the Tzitzica type evolution equations arising in nonlinear optics
Seyed Mehdi Mirhosseini-Alizamini, Hadi Rezazadeh, Mostafa Eslami, Mohammad Mirzazadeh, Alpert Korkmaz
Abstract
In this study, the new extended direct algebraic method is exerted for constructing more general exact solutions of the three nonlinear evolution equations with physical interest namely, the Tzitzeica equation, the Dodd-Bullough-Mikhailor equation and the Liouville equation. By using of an appropriate traveling wave transformation reduces these equations to ODE. We state that this method is excellently a generalized form to obtain solitary wave solutions of the nonlinear evolution equations that are widely used in theoretical physics. The method appears to be easier and faster by means of symbolic computation system.
Topics & Concepts
Nonlinear systemMathematicsOdeTransformation (genetics)Algebraic equationComputationIndependent equationType (biology)Symbolic computationApplied mathematicsAlgebraic numberMathematical analysisDifferential equationPhysicsQuantum mechanicsAlgorithmChemistryBiochemistryEcologyBiologyGeneNonlinear Waves and SolitonsNonlinear Photonic SystemsFractional Differential Equations Solutions