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Multisymplectic geometry, variational integrators, and nonlinear PDEs

Abstract:

This paper presents a geometric-variational approach to continuous and discrete mechanics and field theories. Using multisymplectic geometry, we show that the existence of the fundamental geometric structures as well as their preservation along solutions can be obtained directly from the variational principle. In particular, we prove that a unique multisymplectic structure is obtained by taking the derivative of an action function, and use this structure to prove covariant generalizations of ...

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Publisher copy:
10.1007/s002200050505

Authors


Marsden, JE More by this author
Patrick, GW More by this author
More by this author
Institution:
University of Oxford
Department:
Oxford, MPLS, Mathematical Inst
Journal:
Communications in Mathematical Physics
Volume:
199
Issue:
2
Pages:
351-395
Publication date:
1998-07-15
DOI:
EISSN:
1432-0916
ISSN:
0010-3616
URN:
uuid:02249c2f-2ca8-4581-83d5-222f5bfeff08
Source identifiers:
407506
Local pid:
pubs:407506

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