Choreographies in the discrete nonlinear Schrödinger equations
We study periodic solutions of the discrete nonlinear Schrödinger equation (DNLSE) that bifurcate from a symmetric polygonal relative equilibrium containing n sites. With specialized numerical continuation techniques and a varying physically relevant parameter we can locate interesting orbits, including infinitely many choreographies. Many of the orbits that correspond to choreographies are stable, as indicated by Floquet multipliers that are extracted as part of the numerical continuation scheme, and as verified a posteriori by simple numerical integration. We discuss the physical relevance and the implications of our results.
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- 4.V. Barutello, S. Terracini, Nonlinearity 17, 2015 2004 Google Scholar
- 5.R. Calleja, E. Doedel, C. García-Azpeitia, to appear in Celest. Mech. Dyn. Astron. Google Scholar
- 7.A. Chenciner, J. Gerver, R. Montgomery, C. Simó, Simple choreographic motions of N bodies: a preliminary study, in Geometry, Mechanics, and Dynamics, 60th birthday of J.E. Marsden, edited by P. Newton, P. Holmes, A. Weinstein (Springer-Verlag, 2002) Google Scholar
- 15.P. Kevrekidis, The discrete nonlinear Schrödinger equation. Mathematical Analysis, Numerical Computations and Physical Perspectives (Springer, 2009) Google Scholar
- 24.C. Simó, New Families of Solutions in N-Body Problems, in European Congress of Mathematics (Springer Nature, 2001), pp. 101–115 Google Scholar