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Periodic and homoclinic travelling waves in infinite lattices. (English) Zbl 1213.37106

The author investigates the existence of travelling waves solutions (periodic or homoclinic) for the second order system describing an infinite chain of particles subjected to a potential, and where nearest neighbours are connected by nonlinear oscillators.

MSC:

37K60 Lattice dynamics; integrable lattice equations
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References:

[1] E. Fermi, J. Pasta, S. Ulam, Studies in nonlinear problems, Rept. LA-1940, Los Alamos, Reprinted in: E. Fermi, Collected Papers, vol. II, 1955, pp. 978-988.
[2] Friesecke, G.; Wattis, J., Existence theorem for travelling waves on lattices, Comm. math. phys., 161, 2, 391-418, (1994) · Zbl 0807.35121
[3] Smets, D.; Willem, M., Travelling waves with prescribed speed on infinite lattices, J. funct. anal., 149, 1, 266-275, (1997) · Zbl 0889.34059
[4] Kreiner, C.-F.; Zimmer, J., Travelling waves solutions for the discrete sine-Gordon equation with nonlinear pair-interaction, Nonlinear anal., 70, 3146-3158, (2009) · Zbl 1160.37415
[5] Iooss, G.; Kirchgassner, K., Traveling waves in a chain of coupled nonlinear oscillators, Comm. math. phys., 211, 439-464, (2000) · Zbl 0956.37055
[6] Pankov, A., Travelling waves and periodic oscillations in fermi – pasta – ulam lattices, (2005), Imperial College Press London · Zbl 1088.35001
[7] Bak, S., Periodic traveling waves in chains of oscillators, Commun. math. anal., 3, 1, 19-26, (2007) · Zbl 1171.34028
[8] Rabinowitz, P.H., Homoclinic orbits for a class of Hamiltonian systems, Proc. roy. soc. Edinburgh sect. A, 114, 1-2, 33-38, (1990) · Zbl 0705.34054
[9] Rabinowitz, P.H., Periodic solutions of Hamiltonian systems, Comm. pure appl. math., 31, 2, 157-184, (1978) · Zbl 0358.70014
[10] Rabinowitz, P.H., Some critical point theorems and applications to semilinear elliptic partial differential equations, Ann. sc. norm. super. Pisa cl. sci. (4), 5, 1, 215-223, (1978) · Zbl 0375.35026
[11] Ambrosetti, A.; Rabinowitz, P.H., Dual variational methods in critical point theory and applications, J. funct. anal., 14, 349-381, (1973) · Zbl 0273.49063
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