Group Classification of Generalized Eikonal Equations
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By using a new approach to a group classification, we perform a symmetry analysis of equations of the form uaua = F(t, u, ut) that generalize the well-known eikonal and Hamilton–Jacobi equations.
KeywordsGroup Classification Jacobi Equation Eikonal Equation Symmetry Analysis Generalize Eikonal Equation
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- 1.L. V. Ovsyannikov, Group Analysis of Differential Equations [in Russian], Nauka, Moscow (1978).Google Scholar
- 2.I. Sh. Akhatov, R. K. Gazizov, and N. Kh. Ibragimov, “Nonlocal symmetries. A heuristic approach,” in: VINITI Series in Contemporary Problems in Mathematics. New Trends [in Russian], Vol. 34, VINITI, Moscow (1989), pp. 3–83.Google Scholar
- 3.V. I. Fushchich, V. M. Shtelen', and N. I. Serov, Symmetry Analysis and Exact Solutions of Nonlinear Equations of Mathematical Physics [in Russian], Naukova Dumka, Kiev (1989).Google Scholar
- 4.R. Z. Zhdanov and V. I. Lahno, “Group classification of heat conduction equations with a nonlinear source,” J. Phys. A: Math. Gen., 32, 7405–7418 (1999).Google Scholar
- 5.R. O. Popovych and R. M. Cherniha, “Complete classification of Lie symmetries for systems of nonlinear two-dimensional La-place equations,” in: Group and Analytic Methods in Mathematical Physics [in Ukrainian], Institute of Mathematics, Ukrainian Academy of Sciences, Kiev, (2001), pp. 212–221.Google Scholar
- 6.C. P. Boyer and M. N. Penafiel, “Conformal symmetry of the Hamilton-Jacobi equation and quantization,” Nuovo Cim. B, 31, No. 1, 195–210 (1976).Google Scholar
- 7.W. I. Fushchich and W. M. Shtelen, “The symmetry and some exact solutions of the relativistic eikonal equation,” Lett. Nuovo Cim., 34, No. 16, 498 (1982).Google Scholar
- 8.P. J. Olver, Applications of Lie Groups to Differential Equations, Springer, New York (1986).Google Scholar