Abstract
An approach to the numerical study of the conservative nonlinear dynamical systems is developed based on the method of exact reductions of infinite-dimensional integrable systems on finite-dimensional invariant submanifolds. The phase plane analysis of the corresponding finite-dimensional Hamiltonian dynamical systems makes it possible to identify the initial conditions for such typical solutions as the traveling waves and solitons. The time evolution of these initial conditions is also given by finite-dimensional Hamiltonian dynamical systems.
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Prykarpatsky, A., Brzychczy, S., Samoylenko, V. (2001). About a Finite Dimensional Reduction Method for Conservative Dynamical Systems and Its Applications. In: Krämer, W., von Gudenberg, J.W. (eds) Scientific Computing, Validated Numerics, Interval Methods. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-6484-0_24
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DOI: https://doi.org/10.1007/978-1-4757-6484-0_24
Publisher Name: Springer, Boston, MA
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