Symmetry Reductions, Exact Solutions, and Conservation Laws of a Modified Hunter-Saxton Equation
We study a modified Hunter-Saxton equation from the Lie group-theoretic point of view. The Lie point symmetry generators of the underlying equation are derived. We utilize the Lie algebra admitted by the equation to obtain the optimal system of one-dimensional subalgebras of the Lie algebra of the e...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2013-01-01
|
| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/204746 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832554663129382912 |
|---|---|
| author | Andrew Gratien Johnpillai Chaudry Masood Khalique |
| author_facet | Andrew Gratien Johnpillai Chaudry Masood Khalique |
| author_sort | Andrew Gratien Johnpillai |
| collection | DOAJ |
| description | We study a modified Hunter-Saxton equation from the Lie group-theoretic point of view. The Lie point symmetry generators of the underlying equation are derived. We utilize the Lie algebra admitted by the equation to obtain the optimal system of one-dimensional subalgebras of the Lie algebra of the equation. These subalgebras are then used to reduce the underlying equation to nonlinear third-order ordinary differential equations. Exact traveling wave group-invariant solutions for the equation are constructed by integrating the reduced ordinary differential equations. Moreover, using the variational method, we construct infinite number of nonlocal conservation laws by the transformation of the dependent variable of the underlying equation. |
| format | Article |
| id | doaj-art-c9320f75fb5e40b489da5db3627ecfe3 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-c9320f75fb5e40b489da5db3627ecfe32025-02-03T05:50:54ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/204746204746Symmetry Reductions, Exact Solutions, and Conservation Laws of a Modified Hunter-Saxton EquationAndrew Gratien Johnpillai0Chaudry Masood Khalique1Department of Mathematics, Eastern University, Sri LankaInternational Institute for Symmetry Analysis and Mathematical Modelling, Department of Mathematical Sciences, North-West University, Mafikeng Campus, Private Bag X 2046, Mmabatho 2735, South AfricaWe study a modified Hunter-Saxton equation from the Lie group-theoretic point of view. The Lie point symmetry generators of the underlying equation are derived. We utilize the Lie algebra admitted by the equation to obtain the optimal system of one-dimensional subalgebras of the Lie algebra of the equation. These subalgebras are then used to reduce the underlying equation to nonlinear third-order ordinary differential equations. Exact traveling wave group-invariant solutions for the equation are constructed by integrating the reduced ordinary differential equations. Moreover, using the variational method, we construct infinite number of nonlocal conservation laws by the transformation of the dependent variable of the underlying equation.http://dx.doi.org/10.1155/2013/204746 |
| spellingShingle | Andrew Gratien Johnpillai Chaudry Masood Khalique Symmetry Reductions, Exact Solutions, and Conservation Laws of a Modified Hunter-Saxton Equation Abstract and Applied Analysis |
| title | Symmetry Reductions, Exact Solutions, and Conservation Laws of a Modified Hunter-Saxton Equation |
| title_full | Symmetry Reductions, Exact Solutions, and Conservation Laws of a Modified Hunter-Saxton Equation |
| title_fullStr | Symmetry Reductions, Exact Solutions, and Conservation Laws of a Modified Hunter-Saxton Equation |
| title_full_unstemmed | Symmetry Reductions, Exact Solutions, and Conservation Laws of a Modified Hunter-Saxton Equation |
| title_short | Symmetry Reductions, Exact Solutions, and Conservation Laws of a Modified Hunter-Saxton Equation |
| title_sort | symmetry reductions exact solutions and conservation laws of a modified hunter saxton equation |
| url | http://dx.doi.org/10.1155/2013/204746 |
| work_keys_str_mv | AT andrewgratienjohnpillai symmetryreductionsexactsolutionsandconservationlawsofamodifiedhuntersaxtonequation AT chaudrymasoodkhalique symmetryreductionsexactsolutionsandconservationlawsofamodifiedhuntersaxtonequation |