Symmetry Reductions, Exact Solutions, and Conservation Laws of a Modified Hunter-Saxton Equation | Zendy

A.G. Johnpillai | Zendy; Chaudry Masood Khalique | Zendy

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Symmetry Reductions, Exact Solutions, and Conservation Laws of a Modified Hunter-Saxton Equation

Author(s) -

A.G. Johnpillai,

Chaudry Masood Khalique

Publication year - 2013

Publication title -

abstract and applied analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.228

H-Index - 56

eISSN - 1687-0409

pISSN - 1085-3375

DOI - 10.1155/2013/204746

Subject(s) - mathematics , conservation law , exact differential equation , ordinary differential equation , invariant (physics) , partial differential equation , lie algebra , first order partial differential equation , differential equation , symmetry (geometry) , riccati equation , mathematical analysis , symmetry group , lie group , mathematical physics , pure mathematics , geometry

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

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