Abstract
Abstracts. A method for the group classification of differential equations is proposed. It is based on the determination of all possible cases of linear dependence of certain indeterminates appearing in the determining equations of symmetries of the equation. The method is simple and systematic and applied to a family of hyperbolic equations. Moreover, as the given family contains several known equations with important physical applications, low-order conservation laws of some relevant equations from the family are computed, and the results obtained are discussed with regard to the symmetry integrability of a particular class from the underlying family of hyperbolic equations.
Highlights
The group classification of differential equations, which consists in determining all symmetry classes admitted by an equation according to the values of the parameters or arbitrary functions labelling the given family of differential equations, has been carried out in the literature mostly in a more or less ad hoc manner [1,2,3,4,5,6,7]
It is based on the determination of all possible cases of linear dependence of certain indeterminates appearing in the determining equations for the Lie point symmetry algebra of the given family of equations
Using the symmetry argument related to the structure of (1) together with the above results show that the multipliers Q and corresponding conservation laws of (1) are given for F arbitrary by where p = pðxÞ and q = qðyÞ are arbitrary functions
Summary
The group classification of differential equations, which consists in determining all symmetry classes admitted by an equation according to the values of the parameters or arbitrary functions labelling the given family of differential equations, has been carried out in the literature mostly in a more or less ad hoc manner [1,2,3,4,5,6,7]. Attempts to find a somewhat systematic method for this classification problem has, been made This includes the well-known algebraic method which can be traced back to Lie’s work on symmetry algebras of ordinary differential equations (ODEs), and which has been upgraded or applied in several papers [2, 4, 8,9,10,11]. We propose a new and systematic method for the group classification of differential equations It is based on the determination of all possible cases of linear dependence of certain indeterminates appearing in the determining equations for the Lie point symmetry algebra of the given family of equations. It will naturally be assumed that F is a nonconstant function
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