J. S. Russell, Report on waves In 14th meeting of the British Association for the Advancement of Science, p.390, 1844.

B. J. West, An essay on the importance of being nonlinear, 2013.
DOI : 10.1007/978-3-642-93306-6

A. C. Scott, Nonlinear science, 1999.

L. Brillouin, Wave propagation in periodic structures : electric filters and crystal lattices, Courier Corporation, 2003.

W. Chen and D. L. Mills, Gap solitons and the nonlinear optical response of superlattices, Physical Review Letters, vol.56, issue.2, p.160, 1987.
DOI : 10.1063/1.333982

S. B. Yamgoué, S. Morfu, and P. Marquié, transmission line, Physical Review E, vol.305, issue.3, p.36211, 2007.
DOI : 10.1103/PhysRevE.71.056620

B. Bodo, University of Yaounde I (Cameroon) and Université de Bourgogne (France), 2009.

B. Bodo, S. Morfu, P. Marquié, and M. Rosse, Klein-Gordon electronic network exhibiting supratransmission effect, Electronics Letters, vol.46, issue.2, pp.123-124, 2010.
DOI : 10.1049/el.2010.3200
URL : https://hal.archives-ouvertes.fr/hal-00649683

B. Yousefzadeh and A. Phani, Supratransmission in a disordered nonlinear periodic structure, Journal of Sound and Vibration, vol.380, pp.242-266, 2016.
DOI : 10.1016/j.jsv.2016.06.001

C. Jd-tchinang-tchameu, . Tchawoua, and . Motcheyo, Nonlinear supratransmission of multibreathers in discrete nonlinear Schr??dinger equation with saturable nonlinearities, Wave Motion, vol.65, pp.112-118, 2016.
DOI : 10.1016/j.wavemoti.2016.04.002

J. E. Macías-díaz, Numerical study of the process of nonlinear supratransmission in Riesz space-fractional sine-Gordon equations, Communications in Nonlinear Science and Numerical Simulation, vol.46, pp.89-102, 2017.
DOI : 10.1016/j.cnsns.2016.11.002

A. B. Togueu-motcheyo, J. D. Tchameu, M. S. Siewe, and C. Tchawoua, Homoclinic nonlinear band gap transmission threshold in discrete optical waveguide arrays, Communications in Nonlinear Science and Numerical Simulation, vol.50, pp.29-34, 2017.
DOI : 10.1016/j.cnsns.2017.02.001

J. E. Macías-díaz, Numerical simulation of the nonlinear dynamics of harmonically driven Riesz-fractional extensions of the Fermi???Pasta???Ulam chains, Communications in Nonlinear Science and Numerical Simulation, vol.55, pp.248-264, 2018.
DOI : 10.1016/j.cnsns.2017.07.012

F. Geniet and J. Leon, Energy Transmission in the Forbidden Band Gap of a Nonlinear Chain, Physical Review Letters, vol.123, issue.13, p.134102, 2002.
DOI : 10.1103/PhysRevB.46.578

F. Geniet and J. Leon, Nonlinear supratransmission, Journal of Physics: Condensed Matter, vol.15, issue.17, p.2933, 2003.
DOI : 10.1088/0953-8984/15/17/341
URL : https://hal.archives-ouvertes.fr/hal-00000362

J. Leon, Nonlinear supratransmission as a fundamental instability, Physics Letters A, vol.319, issue.1-2, pp.130-136, 2003.
DOI : 10.1016/j.physleta.2003.10.012
URL : https://hal.archives-ouvertes.fr/hal-00178219

G. Huang, Gap Solitons and Resonant Kinks in One-Dimensional Heisenberg Ferromagnets, Communications in Theoretical Physics, vol.25, issue.4, pp.415-420, 1996.
DOI : 10.1088/0253-6102/25/4/415

B. Z. Essimbi and I. V. Barashenkov, Spatially localized voltage oscillations in an electrical lattice, Journal of Physics D: Applied Physics, vol.35, issue.12, p.1438, 2002.
DOI : 10.1088/0022-3727/35/12/323

M. Remoissenet, Low-amplitude breather and envelope solitons in quasi-one-dimensional physical models, Physical Review B, vol.17, issue.4, p.2386, 1986.
DOI : 10.1088/0022-3719/17/33/009

M. Peyrard and T. Dauxois, Physique des solitons, EDP Sciences, 2012.

D. K. Campbell and M. Peyrard, Chaos and order in non-integrable model field theories, Los Alamos National Lab., NM (USA), 1989.

S. Flach and A. V. Gorbach, Discrete breathers ??? Advances in theory and applications, Physics Reports, vol.467, issue.1-3, pp.1-116, 2008.
DOI : 10.1016/j.physrep.2008.05.002

A. J. Sievers and S. Takeno, Intrinsic Localized Modes in Anharmonic Crystals, Physical Review Letters, vol.30, issue.8, pp.970-973, 1988.
DOI : 10.1103/PhysRevB.30.4853

A. Amo, S. Pigeon, D. Sanvitto, V. G. Sala, R. Hivet et al., Polariton Superfluids Reveal Quantum Hydrodynamic Solitons, Science, vol.100, issue.11, pp.3321167-1170, 2011.
DOI : 10.1103/PhysRevLett.100.110404
URL : http://arxiv.org/pdf/1101.2530

S. Pigeon, I. Carusotto, and C. Ciuti, Hydrodynamic nucleation of vortices and solitons in a resonantly excited polariton superfluid, Physical Review B, vol.83, issue.14, p.144513, 2011.
DOI : 10.1103/PhysRevA.76.013613
URL : https://hal.archives-ouvertes.fr/hal-00494935

L. Gordillo and N. Mujica, Solitons hydrodynamiques non-propagatifs. Résumés des exposés de la 16e Rencontre du Non-Linéaire Paris, p.59, 2013.

A. Hasegawa and F. Tappert, Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. I. Anomalous dispersion, Applied Physics Letters, vol.34, issue.3, pp.142-144, 1973.
DOI : 10.1103/PhysRevLett.29.1308

B. Crosignani and P. D. Porto, Soliton propagation in multimode optical fibers, Optics Letters, vol.6, issue.7, pp.329-330, 1981.
DOI : 10.1364/OL.6.000329

N. J. Doran and K. J. Blow, Solitons in optical communications, IEEE Journal of Quantum Electronics, vol.19, issue.12, pp.1883-1888, 1983.
DOI : 10.1109/JQE.1983.1071806

P. Vandamme, J. Thomine, and P. Gallion, Soliton transmission on optical fibres, Annales Des Télécommunications, pp.79-97, 1995.

D. Mihalache, D. Mazilu, F. Lederer, B. A. Malomed, Y. V. Kartashov et al., Stable Spatiotemporal Solitons in Bessel Optical Lattices, Physical Review Letters, vol.43, issue.2, p.23902, 2005.
DOI : 10.1016/0370-1573(89)90152-X

Y. V. Kartashov, B. A. Malomed, and L. Torner, Solitons in nonlinear lattices, Reviews of Modern Physics, vol.16, issue.1, p.247, 2011.
DOI : 10.1016/j.physleta.2008.04.003

B. Z. Essimbi, A. M. Dikandé, T. C. Kofané, and A. A. Zibi, Asymmetric gap solitons in a non-linear LC transmission line, Physica Scripta, vol.52, issue.1, p.17, 1995.
DOI : 10.1088/0031-8949/52/1/002

S. A. Kiselev and A. J. Sievers, Generation of intrinsic vibrational gap modes in three-dimensional ionic crystals, Physical Review B, vol.25, issue.9, pp.5755-5758, 1997.
DOI : 10.1080/00018737600101392

G. Huang and B. Hu, Asymmetric gap soliton modes in diatomic lattices with cubic and quartic nonlinearity, Physical Review B, vol.55, issue.10, p.5746, 1998.
DOI : 10.1103/PhysRevB.55.6304

A. De-rossi, C. Conti, and S. Trillo, Stability, Multistability, and Wobbling of Optical Gap Solitons, Physical Review Letters, vol.14, issue.1, pp.85-88, 1998.
DOI : 10.1364/OL.14.001071

T. Iizuka and Y. S. Kivshar, Optical gap solitons in nonresonant quadratic media, Physical Review E, vol.81, issue.6, pp.7148-7151, 1999.
DOI : 10.1103/PhysRevLett.81.85

M. Scalora, J. P. Dowling, C. M. Bowden, and M. J. Bloemer, Optical Limiting and Switching of Ultrashort Pulses in Nonlinear Photonic Band Gap Materials, Physical Review Letters, vol.108, issue.10
DOI : 10.1016/0030-4018(94)90647-5

J. Leon and A. Spire, Gap soliton formation by nonlinear supratransmission in Bragg media, Physics Letters A, vol.327, issue.5-6, pp.474-480, 2004.
DOI : 10.1016/j.physleta.2004.05.054
URL : https://hal.archives-ouvertes.fr/hal-00178217

J. E. Macías-díaz and A. Puri, An application of nonlinear supratransmission to the propagation of binary signals in weakly damped, mechanical systems of coupled oscillators, Physics Letters A, vol.366, issue.4-5, pp.447-450, 2007.
DOI : 10.1016/j.physleta.2007.03.076

H. D. Yang, N. G. Alexopoulos, and E. Yablonovitch, Photonic band-gap materials for high-gain printed circuit antennas, IEEE Transactions on Antennas and Propagation, vol.45, issue.1, pp.185-187, 1997.
DOI : 10.1109/8.554261

F. Yang, K. Ma, Y. Qian, and T. Itoh, A uniplanar compact photonic-bandgap (uc-pbg) structure and its applications for microwave circuit. Microwave Theory and Techniques, IEEE Transactions on, issue.8, pp.471509-1514, 1999.

P. Marquié, J. Bilbault, and M. Remoissenet, Observation of nonlinear localized modes in an electrical lattice, Physical Review E, vol.72, issue.6, p.516127, 1995.
DOI : 10.1103/PhysRevLett.72.1777

B. Z. Essimbi, L. Ambassa, and T. C. Kofane, Gap solitons on a coupled nonlinear transmission line, Physica D: Nonlinear Phenomena, vol.106, issue.1-2, pp.207-217, 1997.
DOI : 10.1016/S0167-2789(96)00297-7

O. Bang and M. Peyrard, Generation of high-energy localized vibrational modes in nonlinear Klein-Gordon lattices, Physical Review E, vol.5, issue.4, p.4143, 1996.
DOI : 10.1038/328089a0

T. Taniuti and N. Yajima, Perturbation Method for a Nonlinear Wave Modulation. I, 48] A. Tsurui. Wave modulations in anharmonic lattices. Progress of Theoretical Physics, pp.1369-13721196, 1969.
DOI : 10.1103/PhysRevLett.15.1005

B. Z. Essimbi, Gap Soliton Excitations in a Model of an Electric Circuit, Physica Scripta, vol.67, issue.2, p.164, 2003.
DOI : 10.1238/Physica.Regular.067a00164

T. Dauxois, M. Peyrard, and C. R. Willis, Localized breather-like solution in a discrete Klein-Gordon model and application to DNA, Physica D: Nonlinear Phenomena, vol.57, issue.3-4, pp.267-282, 1992.
DOI : 10.1016/0167-2789(92)90003-6

P. T. Dinda and M. Remoissenet, Breather compactons in nonlinear Klein-Gordon systems, Physical Review E, vol.13, issue.5, p.6218, 1999.
DOI : 10.1103/PhysRevLett.73.1737

J. C. Comte, Exact discrete breather compactons in nonlinear Klein-Gordon lattices, Physical Review E, vol.59, issue.6, p.67601, 2002.
DOI : 10.1103/PhysRevE.59.6105

Y. Liang and Z. Ma, Levinson???s theorem for the Klein-Gordon equation, Physical Review D, vol.92, issue.2, p.565, 1986.
DOI : 10.1007/BF01215276

G. L. Alfimov, E. V. Medvedeva, and D. E. Pelinovsky, Wave Systems with an Infinite Number of Localized Traveling Waves, Physical Review Letters, vol.80, issue.5, p.54103, 2014.
DOI : 10.1103/PhysRevE.84.056606

P. Rosenau and A. Pikovsky, Breathers in strongly anharmonic lattices, Physical Review E, vol.89, issue.2, p.22924, 2014.
DOI : 10.1103/PhysRevLett.70.564

T. Dauxois, M. Peyrard, and C. R. Willis, Discreteness effects on the formation and propagation of breathers in nonlinear Klein-Gordon equations, Physical Review E, vol.47, issue.6, p.484768, 1993.
DOI : 10.1103/PhysRevB.47.14866

M. J. Ablowitz and H. Segur, Solitons and the inverse scattering transform, SIAM, vol.4, 1981.
DOI : 10.1137/1.9781611970883

M. Remoissenet, Waves Called Solitons: Concepts and Experiments, American Journal of Physics, vol.63, issue.4, 1999.
DOI : 10.1119/1.18083

M. Peyrard, The pathway to energy localization in nonlinear lattices, Physica D: Nonlinear Phenomena, vol.119, issue.1-2, pp.184-199, 1998.
DOI : 10.1016/S0167-2789(98)00079-7

I. Ryshik and I. Gradstein, Tables of integrals, series, and products, 1965.

S. Dusuel, P. Michaux, and M. Remoissenet, From kinks to compactonlike kinks, Physical Review E, vol.63, issue.2, p.2320, 1998.
DOI : 10.1119/1.18019

G. Zhou, Y. Duan, and J. Yan, Comparative study of nonlinear localized modes of diatomic chains with two types of quartic nonlinearity, Physical Review B, vol.58, issue.21, p.13977, 1996.
DOI : 10.1103/PhysRevLett.58.160

J. Caputo, J. Leon, and A. Spire, Nonlinear energy transmission in the gap, Physics Letters A, vol.283, issue.1-2, pp.129-135, 2001.
DOI : 10.1016/S0375-9601(01)00192-X
URL : https://hal.archives-ouvertes.fr/hal-00128295

R. Khomeriki and J. Leon, Bistability in the sine-Gordon equation: The ideal switch, Physical Review E, vol.32, issue.5, p.56620, 2005.
DOI : 10.1063/1.90113
URL : https://hal.archives-ouvertes.fr/in2p3-00148953

B. Bodo, S. Morfu, P. Marquié, and B. Z. Essimbi, Noise induced breather generation in a sine???Gordon chain, Journal of Statistical Mechanics: Theory and Experiment, vol.2009, issue.01, p.1026, 2009.
DOI : 10.1088/1742-5468/2009/01/P01026
URL : https://hal.archives-ouvertes.fr/hal-00651499

J. E. Macías-díaz and A. Puri, On the propagation of binary signals in damped mechanical systems of oscillators, Physica D: Nonlinear Phenomena, vol.228, issue.2, pp.112-121, 2007.
DOI : 10.1016/j.physd.2007.02.007

J. Ruiz-ramírez and J. E. Macías-díaz, ON THE PROPAGATION OF BINARY SIGNALS IN A TWO-DIMENSIONAL NONLINEAR LATTICE WITH NEAREST-NEIGHBOR INTERACTIONS, Journal of Nonlinear Mathematical Physics, vol.105, issue.2, pp.127-136, 2010.
DOI : 10.1021/jp004448y

J. E. Macías-díaz, On the controlled propagation of wave signals in a sinusoidally forced two-dimensional continuous Frenkel???Kontorova model, Wave Motion, vol.48, issue.1, pp.13-23, 2011.
DOI : 10.1016/j.wavemoti.2010.06.005

A. B. Togueu-motcheyo, C. Tchawoua, and J. D. Tchameu, Supratransmission induced by waves collisions in a discrete electrical lattice, Physical Review E, vol.88, issue.4, p.40901, 2013.
DOI : 10.1109/PROC.1973.9297

A. B. Togueu-motcheyo, C. Tchawoua, M. S. Siewe, and J. D. Tchameu, Supratransmission phenomenon in a discrete electrical lattice with nonlinear dispersion, Communications in Nonlinear Science and Numerical Simulation, vol.18, issue.4, pp.946-952, 2013.
DOI : 10.1016/j.cnsns.2012.09.005

K. T. Koon, P. Marquié, and P. T. Dinda, Experimental observation of the generation of cutoff solitons in a discrete l c nonlinear electrical line, Phys. Rev. E, issue.5, p.90052901, 2014.

J. Lydon, G. Theocharis, and C. Daraio, Nonlinear resonances and energy transfer in finite granular chains, Physical Review E, vol.91, issue.2, p.23208, 2015.
DOI : 10.1016/j.physleta.2003.10.012

R. Khomeriki, Nonlinear Band Gap Transmission in Optical Waveguide Arrays, Physical Review Letters, vol.19, issue.6, p.63905, 2004.
DOI : 10.1103/PhysRevE.67.056606

H. Susanto, Boundary Driven Waveguide Arrays: Supratransmission and Saddle-Node Bifurcation, SIAM Journal on Applied Mathematics, vol.69, issue.1, pp.111-125, 2008.
DOI : 10.1137/070698828
URL : http://arxiv.org/pdf/0809.3861

H. Susanto and N. Karjanto, CALCULATED THRESHOLD OF SUPRATRANSMISSION PHENOMENA IN WAVEGUIDE ARRAYS WITH SATURABLE NONLINEARITY, Journal of Nonlinear Optical Physics & Materials, vol.90, issue.02, pp.159-165, 2008.
DOI : 10.1103/PhysRevE.69.066618

R. Khomeriki and J. Leon, Light Detectors Bistable Nonlinear Waveguide Arrays, Physical Review Letters, vol.13, issue.24, p.243902, 2005.
DOI : 10.1016/j.physleta.2003.10.012
URL : https://hal.archives-ouvertes.fr/in2p3-00148948

R. Khomeriki and J. Leon, Tristability in the pendula chain, Physical Review E, vol.78, issue.5, p.57202, 2008.
DOI : 10.1103/PhysRevE.75.066604
URL : https://hal.archives-ouvertes.fr/hal-00333881

R. Khomeriki and J. Leon, Gap soliton dynamics in an optical lattice as a parametrically driven pendulum, Physical Review A, vol.80, issue.3, p.33822, 2009.
DOI : 10.1103/PhysRevA.75.063811
URL : https://hal.archives-ouvertes.fr/hal-00419140

P. Anghel-vasilescu, J. Dorignac, F. Geniet, J. Leon, and A. Taki, Generation and dynamics of quadratic birefringent spatial gap solitons, Physical Review A, vol.83, issue.4, p.43836, 2011.
DOI : 10.1137/050648389
URL : https://hal.archives-ouvertes.fr/hal-00628026

D. Chevriaux, R. Khomeriki, and J. Leon, Theory of a Josephson junction parallel array detector sensitive to very weak signals, Physical Review B, vol.73, issue.21, p.73214516, 2006.
DOI : 10.1103/PhysRevLett.84.741
URL : https://hal.archives-ouvertes.fr/in2p3-00149161

R. Khomeriki, J. Leon, and D. Chevriaux, Quantum Hall bilayer digital amplifier, The European Physical Journal B, vol.49, issue.2, pp.213-218, 2006.
DOI : 10.1140/epjb/e2006-00053-9
URL : https://hal.archives-ouvertes.fr/in2p3-00149197

J. E. Macías-díaz and A. Puri, On the transmission of binary bits in discrete Josephson-junction arrays, Physics Letters A, vol.372, issue.30, pp.5004-5010, 2008.
DOI : 10.1016/j.physleta.2008.05.049

R. Khomeriki and J. Leon, Fluxon dynamics in boundary driven Josephson transmission line, Journal of Physics : Conference Series, p.22035, 2009.
DOI : 10.1088/1742-6596/150/2/022035
URL : https://hal.archives-ouvertes.fr/hal-00374420

J. E. Macías-díaz and S. Jerez-galiano, Two finite-difference schemes that preserve the dissipation of energy in a system of modified wave equations. arXiv preprint, 2011.

C. Guarcello, K. Fedorov, D. Valenti, B. Spagnolo, and A. Ustinov, Sinegordon breathers generation in driven long josephson junctions, 2015.

M. Malishava and R. Khomeriki, All-Phononic Digital Transistor on the Basis of Gap-Soliton Dynamics in an Anharmonic Oscillator Ladder, Physical Review Letters, vol.11, issue.10, p.104301, 2015.
DOI : 10.1063/1.4766305

N. N. Akhmediev, A. Ankiewicz, and J. M. Soto-crespo, Multisoliton solutions of the complex ginzburg-landau equation. Physical review letters, p.794047, 1997.

J. Valentin, Modélisation du transport de phonons dans les semi-conducteurs nanostructurés, 2015.