Chaos and integrability in a nonlinear wave equation |
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Authors: | C Grotta Ragazzo |
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Institution: | (1) Instituto de Matemática e Estatística, Universidade de SÃo Paulo, CP 20570, 01498 SÃo Paulo, SP, Brasil;(2) Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, 10012 New York, New York |
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Abstract: | We consider the parametrized family of equations
tt
,u-
xx
u-au+u
2
2
u=O,x(0,L), with Dirichlet boundary conditions. This equation has finite-dimensional invariant manifolds of solutions. Studying the reduced equation to a four-dimensional manifold, we prove the existence of transversal homoclinic orbits to periodic solutions and of invariant sets with chaotic dynamics, provided that =2, 3, 4,.... For =1 we prove the existence of infinitely many first integrals pairwise in involution. |
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Keywords: | Conservative wave equations Hamiltonian systems transversal homoclinic orbits integrability |
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