<abstract xmlns="http://www.w3.org/1999/xhtml"><p>In this paper we study the modified equal-width equation, which is used in handling simulation of a single dimensional wave propagation in nonlinear media with dispersion processes. Lie point symmetries of this equation are computed and used to construct an optimal system of one-dimensional subalgebras. Thereafter using an optimal system of one-dimensional subalgebras, symmetry reductions and new group-invariant solutions are presented. The solutions obtained are cnoidal and snoidal waves. Furthermore, conservation laws for the modified equal-width equation are derived by employing two different methods, the multiplier method and Noether approach.</p></abstract>

In this paper we study the modified equal-width equation, which is used in handling simulation of a single dimensional wave propagation in nonlinear media with dispersion processes. Lie point symmetries of this equation are computed and used to construct an optimal system of one-dimensional subalgebras. Thereafter using an optimal system of one-dimensional subalgebras, symmetry reductions and new group-invariant solutions are presented. The solutions obtained are cnoidal and snoidal waves. Furthermore, conservation laws for the modified equal-width equation are derived by employing two different methods, the multiplier method and Noether approach.

On optimal system, exact solutions and conservation laws of the modified equal-width equation

Applied Mathematics and Nonlinear Sciences

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

In this paper we study the modified equal-width equation, which is used in handling simulation of a single dimensional wave propagation in nonlinear media with...

[ , ]	X₁	X₃
X₁	0	2X₁
X₂	0	0
X₃	-2X₁	0

Ad	X₁	X₂	X₃
X₁	X₁	X₂	-2ɛX₁ + X₃
X₂	X₁	X₂	X₃
X₃	e²^ɛX₁	X₂	X₃

On optimal system, exact solutions and conservation laws of the modified equal-width equation

Publié en ligne: 23 juil. 2018

Pages: 409 - 418

Reçu: 05 mars 2018

Accepté: 23 juil. 2018

DOI: https://doi.org/10.21042/AMNS.2018.2.00031

Mots clés
modified equal-width equation, Lie symmetries, optimal system of one-dimensional subalgebras, cnoidal and snoidal waves, conservation laws

© 2018 C. M. Khalique et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Lie brackets for equation (1)

Adjoint representation of subalgebras

On optimal system, exact solutions and conservation laws of the modified equal-width equation

Publié en ligne: 23 juil. 2018

Pages: 409 - 418

Reçu: 05 mars 2018

Accepté: 23 juil. 2018

DOI: https://doi.org/10.21042/AMNS.2018.2.00031

Mots clésmodified equal-width equation, Lie symmetries, optimal system of one-dimensional subalgebras, cnoidal and snoidal waves, conservation laws

© 2018 C. M. Khalique et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Lie brackets for equation (1)

Adjoint representation of subalgebras

Mots clés
modified equal-width equation, Lie symmetries, optimal system of one-dimensional subalgebras, cnoidal and snoidal waves, conservation laws