arXiv subjects
Publications and source records attributed to Zehra Pinar.
It is well recognized that new types of exact travelling wave solutions to nonlinear partial differential equations can be obtained by modifications of the methods which are in hand. In this study, we extend the class of auxiliary equations using Hermite differential equation so the solution space of nonlinear partial differential equations is extended too.
To obtain new types of exact travelling wave solutions to nonlinear partial differential equations, a number of approximate methods are known in the literature. In this study, we extend the class of auxiliary equations of Fibonnacci&Lucas type equations. The proposed Fibonnacci&Lucas approximation method produces many new solutions. Consequently, we introduce new exact travelling wave solutions of some physical systems in terms of these new solutions of the Fibonacci&Lucas type equation. In addition to using different ansatz, we use determine different balancing principle to obtain optimal solutions.
It is well recognized that in auxiliary equation methods, the exact solutions of different types of auxiliary equations may produce new types of exact travelling wave solutions to nonlinear partial differential equations in hand. In this study, we extend the class of auxiliary equations of classical Bernoulli equation which considered by various researchers [27, 31, 32, 33, 34, 35] to a variable-coefficient Bernoulli type equation. The proposed variable-coefficient Bernoulli type auxiliary equation produces many new solutions comparing to classical Bernoulli equation which produce two solutions only. Consequently, we introduce new exact travelling wave solutions of some physical systems in terms of these new solutions of the variable-coefficient Bernoulli type equation.