By J. Moser
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Extra resources for Dynamical Systems, Theory and Applications
In fact, before the discovery of the soliton, Visscher and collaborators numerical computations (Payton et al. 1967) had revealed “soliton-like” mediated behavior and enhanced heat transport. Solitary waves and solitons, found also in other realms of science, appear as potential “universal” carriers of almost anything (del Rio et al. 2007; Nayanov 1986) (like surf waves/non-topological solitons in the ocean or bores/topological solitons in rivers). Of particular interest to us here is the model-lattice invented by Toda (1989) for which analytical, exact solutions are known.
X1 ; xP 1 ; x2 ; xP 2 ; : : : ; xn ; xP n ; t / D 0I i D 1; n (8) Here " is a small parameter; … is a potential energy of the unperturbed conservative system; the functions fi may be periodical with respect to time. This system may involve friction of any physical nature. It is considered such vibration modes when all positional coordinates of the finite-dimensional non-conservative system are linked. In these modes, the system behaves like a single-DOF conservative one. The periodic solutions could be called Nonlinear normal modes of the non-conservative nonlinear system.
Mat. : The Method of Normal Oscillation for Essentially Nonlinear Systems. : Resonance modes of near-conservative nonlinear systems. Prikl. Mat. : Matching of local expansions in the theory of nonlinear vibrations. J. Sound Vib. : Normal vibrations of a general class of conservative oscillators. Nonlinear Dyn. : Normal vibrations in near-conservative self-exited and viscoelastic nonlinear systems. Nonlinear Dyn. : Dynamical interaction of an elastic system and essentially nonlinear absorber. J.
Dynamical Systems, Theory and Applications by J. Moser