<abstract xmlns="http://www.w3.org/1999/xhtml"><p>In this paper we study a (2+1)-dimensional coupling system with the Korteweg-de Vries equation, which is associated with non-semisimple matrix Lie algebras. Its Lax-pair and bi-Hamiltonian formulation were obtained and presented in the literature. We utilize Lie symmetry analysis along with the (<italic>G</italic>′/<italic>G</italic>)–expansion method to obtain travelling wave solutions of this system. Furthermore, conservation laws are constructed using the multiplier method.</p></abstract>

In this paper we study a (2+1)-dimensional coupling system with the Korteweg-de Vries equation, which is associated with non-semisimple matrix Lie algebras. Its Lax-pair and bi-Hamiltonian formulation were obtained and presented in the literature. We utilize Lie symmetry analysis along with the (G′/G)–expansion method to obtain travelling wave solutions of this system. Furthermore, conservation laws are constructed using the multiplier method.

Travelling waves and conservation laws of a (2+1)-dimensional coupling system with Korteweg-de Vries equation

Applied Mathematics and Nonlinear Sciences

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

In this paper we study a (2+1)-dimensional coupling system with the Korteweg-de Vries equation, which is associated with non-semisimple matrix Lie algebras....

Travelling waves and conservation laws of a (2+1)-dimensional coupling system with Korteweg-de Vries equation

Published Online: Oct 03, 2018

Page range: 241 - 254

Received: Mar 06, 2018

Accepted: Jun 05, 2018

DOI: https://doi.org/10.21042/AMNS.2018.1.00018

Keywords
(2+1)-dimensional coupling system with the Korteweg-de Vries equation, Lie symmetries, (′/)–expansion method, travelling wave solutions, conservation laws

© 2018 C.M. Khalique and I.E. Mhlanga, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

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Travelling waves and conservation laws of a (2+1)-dimensional coupling system with Korteweg-de Vries equation

Published Online: Oct 03, 2018

Page range: 241 - 254

Received: Mar 06, 2018

Accepted: Jun 05, 2018

DOI: https://doi.org/10.21042/AMNS.2018.1.00018

Keywords(2+1)-dimensional coupling system with the Korteweg-de Vries equation, Lie symmetries, (′/)–expansion method, travelling wave solutions, conservation laws

© 2018 C.M. Khalique and I.E. Mhlanga, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Fig. 1

Fig. 2

Fig. 3

Fig. 4

Keywords
(2+1)-dimensional coupling system with the Korteweg-de Vries equation, Lie symmetries, (′/)–expansion method, travelling wave solutions, conservation laws