Math @ Duke

Publications [#244149] of Stephanos Venakides
Papers Published
 Georgieva, A; Kriecherbauer, T; Venakides, S, Wave Propagation and Resonance in a OneDimensional Nonlinear Discrete Periodic Medium,
Siam Journal on Applied Mathematics, vol. 60 no. 1
(January, 1999),
pp. 272294, Society for Industrial & Applied Mathematics (SIAM) [doi]
(last updated on 2019/04/24)
Abstract: We consider wave propagation in a nonlinear infinite diatomic chain of particles as a discrete model of propagation in a medium whose properties vary periodically in space. The particles have alternating masses M1 and M2 and interact in accordance to a general nonlinear force F acting between the nearest neighbors. Their motion is described by the system of equations qqn = 1/M1(F(yn1yn)F(ynyn+1)), qqn+1 = 1/M2(F(ynyn+1)F(yn+1yn+2)), where {yn}n = ∞∞ is the position of the nth particle. Using Fourier series methods and tools from bifurcation theory, we show that, for nonresonant wavenumbers k, this system admits nontrivial smallamplitude traveling wave solutions g and h, depending only on the linear combination z = knωt. We determine the nonlinear dispersion relation. We also show that the system sustains binary oscillations with arbitrarily large amplitude.


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