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Integrability via Functional Expansion for the KMN Model

Department of Physics, University of Craiova, A.I.Cuza 13, 200585 Craiova, Romania
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Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Symmetry 2020, 12(11), 1819; https://doi.org/10.3390/sym12111819
Received: 11 September 2020 / Revised: 28 October 2020 / Accepted: 30 October 2020 / Published: 3 November 2020
(This article belongs to the Section Physics and Symmetry/Asymmetry)
This paper considers issues such as integrability and how to get specific classes of solutions for nonlinear differential equations. The nonlinear Kundu–Mukherjee–Naskar (KMN) equation is chosen as a model, and its traveling wave solutions are investigated by using a direct solving method. It is a quite recent proposed approach called the functional expansion and it is based on the use of auxiliary equations. The main objectives are to provide arguments that the functional expansion offers more general solutions, and to point out how these solutions depend on the choice of the auxiliary equation. To see that, two different equations are considered, one first order and one second order differential equations. A large variety of KMN solutions are generated, part of them listed for the first time. Comments and remarks on the dependence of these solutions on the solving method and on form of the auxiliary equation, are included. View Full-Text
Keywords: functional expansion; traveling waves; KMN equation functional expansion; traveling waves; KMN equation
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MDPI and ACS Style

Constantinescu, R.; Florian, A. Integrability via Functional Expansion for the KMN Model. Symmetry 2020, 12, 1819. https://doi.org/10.3390/sym12111819

AMA Style

Constantinescu R, Florian A. Integrability via Functional Expansion for the KMN Model. Symmetry. 2020; 12(11):1819. https://doi.org/10.3390/sym12111819

Chicago/Turabian Style

Constantinescu, Radu, and Aurelia Florian. 2020. "Integrability via Functional Expansion for the KMN Model" Symmetry 12, no. 11: 1819. https://doi.org/10.3390/sym12111819

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