Abstract
In numerical and physical experiments it is often observed that finite and infinite dimensional systems exhibit a low dimensional behaviour, in the sense that the dynamics looks as if it can be described with a few parameters. Often a spatially coherent structure is characteristic for the phenomenon. A well known example is a solitary wave, characterized by its phase and its amplitude. In this paper we consider a Hamiltonian system (or a Poisson system), that has an additional constant of motion (besides the Hamiltonian). We show coherent structures in such a system, by describing some solutions with 2 parameters, induced by the constant of motion. Further we demonstrate that the coherent structures survive even in cases where a small perturbation, such as dissipation, is present. This is demonstrated in some detail for a spherical pendulum with uniform friction, for the Korteweg-de Vries equation with uniform damping and for the Korteweg-de Vries-Burgers equation.
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References
G. Derks, E. van Groesen, and T. Valkering. Approximation in a damped Hamiltonian system by successive relative equilibria. In preparation,1990.
E. van Groesen, F.P.H. van Beckum, and T.P. Valkering. Decay of travelling waves in dissipative Poisson systems. ZAMP, 41, 1990.
E. van Groesen. Structures and methods of infinite dimensional dynamical systems, part III. North-Holland, 1990.
A. Hasegawa. Self-organization processes in continuous media. Advances in Physics, 34, 1985.
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© 1990 Kluwer Academic Publishers
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Derks, G., van Groesen, E., Valkering, T. (1990). Decay of coherent structures in damped Hamiltonian systems. In: Dijksman, J.F., Nieuwstadt, F.T.M. (eds) Integration of Theory and Applications in Applied Mechanics. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-2125-2_24
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DOI: https://doi.org/10.1007/978-94-009-2125-2_24
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-7456-8
Online ISBN: 978-94-009-2125-2
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