Citation: Jorge E. Macías-Díaz, Anastasios Bountis, Helen Christodoulidi. Energy transmission in Hamiltonian systems of globally interacting particles with Klein-Gordon on-site potentials[J]. Mathematics in Engineering, 2019, 1(2): 343-358. doi: 10.3934/mine.2019.2.343
[1] | Remoissenet M (2013) Waves Called Solitons: Concepts and Experiments, 3 Eds., New York: Springer Science & Business Media. |
[2] |
Lomdahl PS, Soerensen OH, Christiansen PL (1982) Soliton excitations in Josephson tunnel junctions. Phys Rev B 25: 5737. doi: 10.1103/PhysRevB.25.5737
![]() |
[3] | Makhankov VG, Bishop AR, Holm DD (1995) Nonlinear Evolution Equations and Dynamical Systems Needs' 94. New York: World Scientific. |
[4] |
Geniet F, Leon J (2002) Energy transmission in the forbidden band gap of a nonlinear chain. Phys Rev Lett 89: 134102. doi: 10.1103/PhysRevLett.89.134102
![]() |
[5] |
Chevriaux D, Khomeriki R, Leon J (2006) Theory of a Josephson junction parallel array detector sensitive to very weak signals. Phys Rev B 73: 214516. doi: 10.1103/PhysRevB.73.214516
![]() |
[6] |
Geniet F, Leon J (2003) Nonlinear supratransmission. J Phys: Condens Matter 15: 2933–2949. doi: 10.1088/0953-8984/15/17/341
![]() |
[7] |
Khomeriki R, Lepri S, Ruffo S (2004) Nonlinear supratransmission and bistability in the Fermi- Pasta-Ulam model. Phys Rev E 70: 066626. doi: 10.1103/PhysRevE.70.066626
![]() |
[8] |
Leon J, Spire A (2004) Gap soliton formation by nonlinear supratransmission in Bragg media. Phys Lett A 327: 474–480. doi: 10.1016/j.physleta.2004.05.054
![]() |
[9] |
Khomeriki R, Leon J (2005) Bistability in the sine-Gordon equation: The ideal switch. Phys Rev E 71: 056620. doi: 10.1103/PhysRevE.71.056620
![]() |
[10] |
Macías-Díaz JE, Medina-Ramírez I (2009) Nonlinear supratransmission and nonlinear bistability in a forced linear array of anharmonic oscillators: A computational study. Int J Mod Phys C 20: 1911–1923. doi: 10.1142/S0129183109014813
![]() |
[11] | Macías-Díaz JE, Ruiz-Ramírez J, Flores-Oropeza LA ( 2009) Computational study of the transmission of energy in a two-dimensional lattice with nearest-neighbor interactions. Int J Mod Phys C 20: 1933–1943. |
[12] |
Bodo B, Morfu S, Marquié P, et al. (2010) Klein-Gordon electronic network exhibiting supratransmission effect. Electron Lett 46: 123–124. doi: 10.1049/el.2010.3200
![]() |
[13] |
Tchinang Tchameu JD, Tchawoua C, Togueu Motcheyo AB (2016) Nonlinear supratransmission of multibreathers in discrete nonlinear Schrödinger equation with saturable nonlinearities. Wave Motion 65: 112–118. doi: 10.1016/j.wavemoti.2016.04.002
![]() |
[14] |
Togueu Motcheyo AB, Tchinang Tchameu JD, Siewe Siewe M, et al. (2017) Homoclinic nonlinear band gap transmission threshold in discrete optical waveguide arrays. Commun Nonlinear Sci 50: 29–34. doi: 10.1016/j.cnsns.2017.02.001
![]() |
[15] |
Togueu Motcheyo AB, Tchinang Tchameu JD, Fewo SI, et al. (2017) Chameleon's behavior of modulable nonlinear electrical transmission line. Commun Nonlinear Sci 53: 22–30. doi: 10.1016/j.cnsns.2017.04.031
![]() |
[16] |
Coronel-Escamilla A, Gómez-Aguilar JF, Alvarado-Méndez E, et al. (2016) Fractional dynamics of charged particles in magnetic fields. Int J Mod Phys C 27: 1650084. doi: 10.1142/S0129183116500844
![]() |
[17] |
Benetti FPC, Ribeiro-Teixeira AC, Pakter R, et al. (2014) Nonequilibrium stationary states of 3D self-gravitating systems. Phys Rev Lett 113: 100602. doi: 10.1103/PhysRevLett.113.100602
![]() |
[18] | Miloshevich G, Nguenang JP, Dauxois T, et al. (2017) Traveling solitons in long-range oscillator chains. J Phys A: Math Theor 50: 12LT02. |
[19] |
Campa A, Dauxois T, Ruffo S (2009) Statistical mechanics and dynamics of solvable models with long-range interactions. Phys Rep 480: 57–159. doi: 10.1016/j.physrep.2009.07.001
![]() |
[20] |
Miele A, Dekker J (2008) Long-range chromosomal interactions and gene regulation. Mol Biosyst 4: 1046–1057. doi: 10.1039/b803580f
![]() |
[21] |
Christodoulidi H, Tsallis C, Bountis T (2014) Fermi-Pasta-Ulam model with long-range interactions: Dynamics and thermostatistics. Europhys Lett 108: 40006. doi: 10.1209/0295-5075/108/40006
![]() |
[22] | Christodoulidi H, Bountis T, Tsallis C, et al. (2016) Dynamics and statistics of the Fermi-Pasta- Ulam $\beta$-model with different ranges of particle interactions. J Stat Mech: Theory Exp 12: 123206. |
[23] |
Macías-Díaz JE, Bountis A (2018) Supratransmission in $\beta$-Fermi-Pasta-Ulam chains with different ranges of interactions. Commun Nonlinear Sci 63: 307–321. doi: 10.1016/j.cnsns.2018.04.007
![]() |
[24] |
Tarasov VE (2006) Continuous limit of discrete systems with long-range interaction. J Phys A: Math Gen 39: 14895–14910. doi: 10.1088/0305-4470/39/48/005
![]() |
[25] |
Macías-Díaz JE (2018) An explicit dissipation-preserving method for Riesz space-fractional nonlinear wave equations in multiple dimensions. Commun Nonlinear Sci 59: 67–87. doi: 10.1016/j.cnsns.2017.10.019
![]() |
[26] |
Chendjou GNB, Nguenang JP, Trombettoni A, et al. (2018) Fermi-Pasta-Ulam chains with harmonic and anharmonic long-range interactions. Communi Nonlinear Sci 60: 115–127. doi: 10.1016/j.cnsns.2018.01.006
![]() |
[27] |
Macías-Díaz JE, Puri A (2008) An energy-based computational method in the analysis of the transmission of energy in a chain of coupled oscillators. J Comput Appl Math 214: 393–405. doi: 10.1016/j.cam.2007.03.004
![]() |
[28] |
Macías-Díaz JE (2010) On the simulation of the energy transmission in the forbidden band-gap of a spatially discrete double sine-Gordon system. Comput Phys Commun 181: 1842–1849. doi: 10.1016/j.cpc.2010.07.007
![]() |
[29] |
Christodoulidi H, Bountis T, Drossos L (2018) The effect of long-range interactions on the dynamics and statistics of 1D Hamiltonian lattices with on-site potential. Eur Phys J Spec Top 227: 563–573. doi: 10.1140/epjst/e2018-00003-9
![]() |