Abstract
In this article, the functional variable method (fvm for short) is introduced to establish new exact travelling solutions of the combined KdV–mKdV equation. The technique of the homogeneous balance method is used in second stage to handle the appropriated solutions. We show that, the method is straightforward and concise for several kinds of nonlinear problems. Many new exact travelling wave solutions are successfully obtained.
Highlights
There are several forms of nonlinear partial differential equations that have been presented in the past decades to investigate new exact solutions
For the first case study, we obtained the limited solutions using the partial structures for the function h4 = 0
For the second case study, we introduced the results obtained for the partial structures to solve the KdV–mKdV nonlinear differential equation for the full structures in the presence of the function h4 ≠ 0
Summary
There are several forms of nonlinear partial differential equations that have been presented in the past decades to investigate new exact solutions. Zerarka is Professor of Physics and Applied Mathematics at the University Med Khider at Biskra, Algeria He obtained his PhD from the University of Bordeaux, France. His domain of interest is theoretical physics and applied mathematics He has been teaching and conducting research since 1981, has widely published in international journals and he is the author and co-author of numerous refereed papers. He is the reviewer of numerous papers (Elsevier, Taylor and Francis, Wiley, Springer, Inderscience, Academicjournals and more). He is an active member of the Academy of Science, New York
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