The Cartan-Monge geometric approach to the characteristic method for nonlinear partial differential equations of the first and higher orders |
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| Authors: | D L Blackmore N K Prykarpats’ka V H Samoilenko E Wachnicki M Pytel-Kudela |
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| Institution: | (1) New Jersey Institute of Technology, Newark, NJ, USA;(2) AGH University of Science and Technology, Krakow, Poland;(3) Shevchenko Kyiv National University, Kyiv;(4) Institute of Mathematics, Pedagogic Academy, Krakow, Poland |
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| Abstract: | We develop the Cartan-Monge geometric approach to the characteristic method for nonlinear partial differential equations of
the first and higher orders. The Hamiltonian structure of characteristic vector fields related with nonlinear partial differential
equations of the first order is analyzed, and tensor fields of special structure are constructed for defining characteristic
vector fields naturally related with nonlinear partial differential equations of higher orders.
Published in Neliniini Kolyvannya, Vol. 10, No. 1, pp. 26–36, January–March, 2007. |
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