Symmetries and Conservation Laws of the System: ux= vwx, vy= u wy, uv+wxx+wyy=0
Tóm tắt
After a short exposition of the theory of local and nonlocal symmetries and conservation laws for systems of PDE’s, results on these and the recursion operator are listed for the system of PDE’s ux=vwx, vy=uwy, uv+wxx+wyy=0. In between the methods of computation are explained.
Tài liệu tham khảo
van Bemmelen, T.: The symmetry equation package for reduce, Intern. Report No. 1053, Faculty of Applied Mathematics, University of Twente, Enschede, The Netherlands, 1991.
van Bemmelen, T., Gragert, P. K. H., Kersten, P. H. M., and Sym, A. M.: Symmetries and conservation laws of the system: u x = vw x , v y = uw y , uw + w xx + w yy = 0, to appear as Intern. Report, Faculty of Applied Mathematics, University of Twente, Enschede, The Netherlands.
Gragert, P. K. H.: Symbolic computations in prolongation theory, PhD thesis, University of Twente, Enschede, The Netherlands, 1981.
Kersten, P. H. M. and Krasil'shchik, I. S.: Deformations of differential equations and recursion operators, to appear, in Rassias and Prastaro (eds.), Geometry of Differential Equations, World Scientific, Singapore, 1992.
Kersten, P. H. M.: Infinitesimal symmetries: A computational approach, CWI Tract, Centre for Mathematics and Computer Science, Amsterdam, The Netherlands, 1987.
Krasil'shchik, I. S.: Some new cohomological invariants for nonlinear differential equations, to appear in Differential Geometry and its Applications.
Krasil'shchik, I. S. and Vinogradov, A. M.: Nonlocal trends in the geometry of differential equations: Symmetries, conservation laws, and Bäcklund transformations, Acta Appl. Math. 15 (1989), 161–209.
Olver, P. J.: Applications of Lie Groups to Differential Equations, Springer, New York, 1987.
Roelofs, G. H. M.: The integrator package for reduce, Intern. Report No. 942, Faculty of Applied Mathematics, University of Twente, Enschede, The Netherlands, 1991.
Roelofs, G. H. M.: The tools package for reduce, Report, Faculty of Applied Mathematics, University of Twente, Enschede, The Netherlands, 1991.
Sym, A. M.: Private communications.
Ten Eikelder, H. M. M.: Symmetries for dynamical and hamiltonian systems, CWI Tract, Centre for Mathematics and Computer Science, Amsterdam, The Netherlands, 1985.
Vinogradov, A. M.: Symmetries and conservation laws of partial differential equations: Basic notions and results, Acta Appl. Math. 15 (1989), 3–21.