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Symmetries and Conservation Laws of the System: ux= vwx, vy= u wy, uv+wxx+wyy=0

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Abstract

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.

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References

  1. van Bemmelen, T.: The symmetry equation package for reduce, Intern. Report No. 1053, Faculty of Applied Mathematics, University of Twente, Enschede, The Netherlands, 1991.

    Google Scholar 

  2. 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.

  3. Gragert, P. K. H.: Symbolic computations in prolongation theory, PhD thesis, University of Twente, Enschede, The Netherlands, 1981.

    Google Scholar 

  4. 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.

    Google Scholar 

  5. Kersten, P. H. M.: Infinitesimal symmetries: A computational approach, CWI Tract, Centre for Mathematics and Computer Science, Amsterdam, The Netherlands, 1987.

    Google Scholar 

  6. Krasil'shchik, I. S.: Some new cohomological invariants for nonlinear differential equations, to appear in Differential Geometry and its Applications.

  7. 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.

    Google Scholar 

  8. Olver, P. J.: Applications of Lie Groups to Differential Equations, Springer, New York, 1987.

    Google Scholar 

  9. Roelofs, G. H. M.: The integrator package for reduce, Intern. Report No. 942, Faculty of Applied Mathematics, University of Twente, Enschede, The Netherlands, 1991.

    Google Scholar 

  10. Roelofs, G. H. M.: The tools package for reduce, Report, Faculty of Applied Mathematics, University of Twente, Enschede, The Netherlands, 1991.

    Google Scholar 

  11. Sym, A. M.: Private communications.

  12. Ten Eikelder, H. M. M.: Symmetries for dynamical and hamiltonian systems, CWI Tract, Centre for Mathematics and Computer Science, Amsterdam, The Netherlands, 1985.

    Google Scholar 

  13. Vinogradov, A. M.: Symmetries and conservation laws of partial differential equations: Basic notions and results, Acta Appl. Math. 15 (1989), 3–21.

    Google Scholar 

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Authors and Affiliations

  1. Faculty of Applied Mathematics, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands

    T. van Bemmelen, P. K. H. Gragert & P. H. M. Kersten

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  1. T. van Bemmelen
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  2. P. K. H. Gragert
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  3. P. H. M. Kersten
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van Bemmelen, T., Gragert, P.K.H. & Kersten, P.H.M. Symmetries and Conservation Laws of the System: ux= vwx, vy= u wy, uv+wxx+wyy=0. Acta Applicandae Mathematicae 47, 79–99 (1997). https://doi.org/10.1023/A:1005798508219

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