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Basis of Joint Invariants for (1 + 1) Linear Hyperbolic Equations (2002)

by I K Johnpillai ,  F M Mahomed ,  C Wafo Soh
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Abstract:

We obtain a basis of joint or proper di#erential invariants for the scalar linear hyperbolic partial di#erential equation in two independent variables by the infinitesimal method. The joint invariants of the hyperbolic equation consist of combinations of the coe#cients of the equation and their derivatives which remain invariant under equivalence transformations of the equation and are useful for classification purposes. We also derive the operators of invariant di#erentiation for this type of equation. Furthermore, we show that the other di#erential invariants are functions of the elements of this basis via their invariant derivatives. Applications to hyperbolic equations that are reducible to their Lie canonical forms are provided. 1

Citations

243 Linear and Nonlinear Waves – Whitham - 1974
52 Partial Differential Equations – Garabedian - 1998
32 Partial Differential Equations of Applied Mathematics – Zauderer - 1989
23 Partial Differential Equations for Scientists and Engineers – Farlow - 1993
14 Klassifikation und Integration von gewohnlichen Differentialgleichungen zwischen x, y, die eine Gruppe von Transformationen gestatten I – Lie - 1924
9 unknown title – Lie - 1968
8 Partial Differential Equations: Analytical Solution Techniques – Kevorkian - 2000
6 Partial dierential equations – Garabedian - 1964
5 Elementary Lie group analysis and ordinary differential equations – Ibragimov - 1999
3 Partial Di#erential Equations of Applied Mathematics, A Wiley-Interscience – Zauderer - 1983
2 Partial Di#erential Equations for Scientists & Engineers – Farlow - 1982
1 Infinitesimal Method in the Theory of Invariants of Algebraic and – Ibragimov - 1997
1 Mahomed F M, Singular Invariant Equation for the (1 + 1) Fokker – Johnpillai
1 Partial Di#erential Equations: Analytical Solution Techniques, The – Kevorkian - 1990
1 Recherches sur le calcul integral aux di#erences partielles, Memoires de l'Academie Royale des Sciences de Paris 1773/77, 341--402 – Laplace - 1966
1 Group Properties of the Chaplygin Equation – Ovsiannikov - 1960
1 Group Analysis of Di#erential Equations, English translation by – Ovsiannikov - 1982
1 Hyperbolic Partial Di#erential Equations, Advances in Hyperbolic Partial Di#erential Equations – Witten - 1983
1 Mahomed F M, Singular Invariant Equation for the (1 – Johnpillai
1 Group Analysis of Differential Equations, English translation by – Ovsiannikov - 1982
1 Hyperbolic Partial Differential Equations, Advances in Hyperbolic Partial Differential Equations – Witten - 1983
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