<abstract xmlns="http://www.w3.org/1999/xhtml"><p>In this paper we study a nonlinear multi-dimensional partial differential equation, namely, a generalized second extended (3+1)-dimensional Jimbo-Miwa equation. We perform symmetry reductions of this equation until it reduces to a nonlinear fourth-order ordinary differential equation. The general solution of this ordinary differential equation is obtained in terms of the Weierstrass zeta function. Also travelling wave solutions are derived using the simplest equation method. Finally, the conservation laws of the underlying equation are computed by employing the conservation theorem due to Ibragimov, which include conservation of energy and conservation of momentum laws.</p></abstract>

In this paper we study a nonlinear multi-dimensional partial differential equation, namely, a generalized second extended (3+1)-dimensional Jimbo-Miwa equation. We perform symmetry reductions of this equation until it reduces to a nonlinear fourth-order ordinary differential equation. The general solution of this ordinary differential equation is obtained in terms of the Weierstrass zeta function. Also travelling wave solutions are derived using the simplest equation method. Finally, the conservation laws of the underlying equation are computed by employing the conservation theorem due to Ibragimov, which include conservation of energy and conservation of momentum laws.

Solutions and conservation laws of a generalized second extended (3+1)-dimensional Jimbo-Miwa 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 nonlinear multi-dimensional partial differential equation, namely, a generalized second extended (3+1)-dimensional Jimbo-Miwa...

Solutions and conservation laws of a generalized second extended (3+1)-dimensional Jimbo-Miwa equation

Published Online: Dec 01, 2018

Page range: 459 - 474

Received: Aug 06, 2018

Accepted: Nov 06, 2018

DOI: https://doi.org/10.2478/AMNS.2018.2.00036

Keywords
A generalized second extended (3+1)-dimensional Jimbo-Miwa equation, Lie point symmetries, exact solutions, simplest equation method, conservation laws

© 2018 Letlhogonolo Daddy Moleleki et al., published by Sciendo

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

Solutions and conservation laws of a generalized second extended (3+1)-dimensional Jimbo-Miwa equation

Published Online: Dec 01, 2018

Page range: 459 - 474

Received: Aug 06, 2018

Accepted: Nov 06, 2018

DOI: https://doi.org/10.2478/AMNS.2018.2.00036

KeywordsA generalized second extended (3+1)-dimensional Jimbo-Miwa equation, Lie point symmetries, exact solutions, simplest equation method, conservation laws

© 2018 Letlhogonolo Daddy Moleleki et al., published by Sciendo

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

Keywords
A generalized second extended (3+1)-dimensional Jimbo-Miwa equation, Lie point symmetries, exact solutions, simplest equation method, conservation laws