The Cartan-Monge geometric approach to the characteristic method for nonlinear partial differential equations of the first and higher orders

D. L. Blackmore; N. K. Prykarpats'Ka; V. H. Samoilenko; E. Wachnicki; M. Pytel-Kudela

doi:10.1007/s11072-007-0003-3

The Cartan-Monge geometric approach to the characteristic method for nonlinear partial differential equations of the first and higher orders

D. L. Blackmore, N. K. Prykarpats'Ka, V. H. Samoilenko, E. Wachnicki, M. Pytel-Kudela

Mathematical Sciences

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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.

Original language	English (US)
Pages (from-to)	22-31
Number of pages	10
Journal	Nonlinear Oscillations
Volume	10
Issue number	1
DOIs	https://doi.org/10.1007/s11072-007-0003-3
State	Published - Jan 2007

All Science Journal Classification (ASJC) codes

Mathematics (miscellaneous)

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10.1007/s11072-007-0003-3

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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.",

author = "Blackmore, {D. L.} and Prykarpats'Ka, {N. K.} and Samoilenko, {V. H.} and E. Wachnicki and M. Pytel-Kudela",

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AU - Blackmore, D. L.

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AU - Samoilenko, V. H.

AU - Wachnicki, E.

AU - Pytel-Kudela, M.

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N2 - 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.

AB - 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.

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The Cartan-Monge geometric approach to the characteristic method for nonlinear partial differential equations of the first and higher orders

Abstract

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