Excitation thresholds for nonlinear localized modes on lattices

Nonlinearity

Volumn 12, Issue 3, 1999, Pages 673-691

  Weinstein, M I ^a,b  

^a UNIVERSITY OF MICHIGAN   (United States)

^b LUCENT TECHNOLOGIES   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0033130275     PISSN: 09517715     EISSN: None     Source Type: Journal    
DOI: 10.1088/0951-7715/12/3/314     Document Type: Article

References (30)

1. Aceves A B, De Angelis C, Luther G G and Rubenchik A M 1994 Multi-dimensional solitons in fibre arrays Opt. Lett. 19 1186
2. Aceves A B, Luther G G, De Angelis C, Rubenchik A M and Turitsyn S K 1995 Energy localization in nonlinear fibre arrays: collapse-effect compressor Phys. Rev. Lett. 75 73-6
3. Aubry S 1997 Breathers in nonlinear lattices: Existence, linear stability and quantization Physica D 103 201-50
4. Bang O, Rasmussen J J and Christiansen P L 1994 Subcritical localization in the discrete nonlinear Schrödinger equation with arbitrary power nonlinearity Nonlinearity 7 205-18
5. Brezis H and Lieb E 1984 Commun. Math. Phys. 96 97
6. Buryak A V and Akhmediev N N 1995 Stationary pulse propagation in n-core nonlinear fibre arrays IEEE J. Quantum Electron. 31 682
7. Cazenave T and Lions P-L 1982 Orbital stability of standing waves for some nonlinear Schrödinger equations Commun. Math. Phys. 85 549-61
8. Colin T and Weinstein M I 1996 On the ground states of vector nonlinear Schrödinger equations Ann. Inst. Henri Poincaré 65 57-79
9. Eilbeck J C, Lomdahl P S and Scott A C 1985 The discrete self-trapping equation Physica D 16 318-38
10. Eisenberg H S, Silberberg Y, Morandotti R, Boyd A R and Aitchison J S 1998 Discrete spatial optical solitons in waveguide arrays Phys. Rev. Lett. 81 3383
11. Flach S 1996 Tangent bifurcation of band edge plane waves, dynamical symmetry breaking and vibrational localization Physica D 91 223
12. Flach S 1998 Breathers on latttices with long range interaction Phys. Rev. E 58 R4116
13. Flach S, Kladko K and MacKay R S 1997 Energy thresholds for discrete breathers in one-, two-, and three-dimensional lattices Phys. Rev. Lett. 78 1207-10
14. Flach S and Willis C R 1998 Discrete breathers Phys. Rep. 295 181-264
15. Friedman A 1969 Partial Differential Equations (New York: Holt Rinehart and Winston)
16. Ginibre J and Velo G 1979 On a class of nonlinear Schrödinger equations J. Func. Anal 32 1-71
17. Glassey R T 1977 On the blowing up of solutions to the Cauchy problem for nonlinear Schrödinger equations J. Math. Phys. 18 1794-7
18. Kato T 1987 On nonlinear Schrödinger equations Ann. Inst. Henri Poincaré, Phys. Théor. 46 113-29
19. Laedke E W, Spatschek K H and Turitsyn S K 1994 Stability of discrete solitons and quasicollapse to intrinsically localized modes Phys. Rev. Lett. 73 1055-9
20. Laedke E W, Spatschek K H, Turitsyn S K and Mezentsev V K 1995 Analytic criterion for soliton instability in a nonlinear fibre array Phys. Rev. E 52 5549-54
21. MacKay R S and Aubry S 1994 Proof of existence of breathers for time-reversible or Hamiltonian networks of weakly coupled oscillators Nonlinearity 7 1623-43
22. Lions P-L 1984 The concentration compactnes principle in the calculus of variations 1: The locally compact case Ann. Inst. Henri Poincaré, Analyse Nonlinéaire 1 223
23. Malomed B and Weinstein M I 1996 Soliton dynamics in the discrete nonlinear Schrödinger equation Phys. Lett. A 220 91
24. Strauss W A 1974 Dispersion of low-energy waves for two conservative equations Archive Rat. Mech. Anal. 55 86-92
25. Vlasov V N, Petrishchev I A and Talanov V I 1971 Isv. Rad. 14 1353
26. Weinstein M I 1986 Lyapunov stability of ground states of nonlinear dispersive evolution equations Commun. Pure Appl. Math. 39 51
27. Weinstein M I and Yeary B 1996 Excitation and dynamics of soliton pulses in optical fibre arrays Phys. Lett. A 222 157-62
28. Weinstein M I 1983 Nonlinear Schrödinger equations and sharp interpolation estimates Commun. Math. Phys. 87 567
29. Weinstein M I 1989 The nonlinear Schrödinger equation - Singularity formation, stability and dispersion Contemporary Mathematics 99 (New York: AMS)
30. Yeary B 1997 Coupled nonlinear Schrödinger equations Thesis, University of Michigan