Jonas Veenstra, Oleksandr Gamayun, Martin Brandenbourger, Freek van Gorp, Hans Terwisscha-Dekker, Jean-Sébastien Caux, Corentin Coulais, “Nonreciprocal Breathing Solitons”, Phys. Rev. X, 15:3 (2025)
Oleksiy O. Vakhnenko, Vyacheslav O. Vakhnenko, Andriy P. Verchenko, “Physical insight into the semi-discrete nonlinear integrable systems with the true and false multicomponentness”, Chaos, Solitons & Fractals, 200 (2025), 117043
Oleksiy O. Vakhnenko, Vyacheslav O. Vakhnenko, Andriy P. Verchenko, “Dipole–monopole alternative as the precursor of pseudo-excitonic chargeless half-mode in an integrable nonlinear exciton–phonon system on a regular one-dimensional lattice”, Chaos, Solitons & Fractals, 170 (2023), 113306
Oleksiy O. Vakhnenko, “Davydov–Kyslukha model as the starting point in the development of integrable multi-component nonlinear dynamical systems on quasi-one-dimensional lattices”, Low Temperature Physics, 48:11 (2022), 962
Oleksiy O. Vakhnenko, “Four-component integrable systems inspired by the Toda and the Davydov–Kyslukha models”, Wave Motion, 88 (2019), 1
A. G. Litvak, V. A. Mironov, S. A. Skobelev, L. A. Smirnov, “Peculiarities of the Self-Action of Inclined Wave Beams Incident on a Discrete System of Optical Fibers”, J. Exp. Theor. Phys., 126:1 (2018), 21
Zhi-Yuan Sun, Shmuel Fishman, Avy Soffer, “Soliton trapping in a disordered lattice”, Phys. Rev. E, 92:1 (2015)
Lev N. Lupichev, Alexander V. Savin, Vasiliy N. Kadantsev, Springer Series in Synergetics, Synergetics of Molecular Systems, 2015, 243
Oleksiy O. Vakhnenko, “Nonlinear integrable model of Frenkel-like excitations on a ribbon of triangular lattice”, Journal of Mathematical Physics, 56:3 (2015)
Zhi-Yuan Sun, Shmuel Fishman, Avy Soffer, “Soliton mobility in disordered lattices”, Phys. Rev. E, 92:4 (2015)
A. Chowdury, A. Ankiewicz, N. Akhmediev, “Solutions of the higher-order Manakov-type continuous and discrete equations”, Phys. Rev. E, 90:1 (2014)
Dragan Toprek, Zoran Ivić, Darko Kapor, Sreten Lekić, “Stationary polarons in discrete molecular chains”, Int J of Quantum Chemistry, 113:10 (2013), 1522
Zhang D.-J., Chen Sh.-T., “Symmetries for the Ablowitz-Ladik Hierarchy: Part II. Integrable Discrete Nonlinear Schrodinger Equations and Discrete AKNS Hierarchy”, Stud Appl Math, 125:4 (2010), 419–443
Oleksiy O. Vakhnenko, “Inverse scattering transform for the nonlinear Schrödinger system on a zigzag-runged ladder lattice”, Journal of Mathematical Physics, 51:10 (2010)
Aristophanes Dimakis, Folkert Müller-Hoissen, “Solutions of matrix NLS systems and their discretizations: a unified treatment”, Inverse Problems, 26:9 (2010), 095007
Edward Arévalo, “Solitary wave solutions as a signature of the instability in the discrete nonlinear Schrödinger equation”, Physics Letters A, 373:39 (2009), 3541
Oleksiy O. Vakhnenko, “Enigma of probability amplitudes in Hamiltonian formulation of integrable semidiscrete nonlinear Schrödinger systems”, Phys. Rev. E, 77:2 (2008)
Josselin Garnier, Fatkhulla Kh. Abdullaev, Mario Salerno, “Solitons in strongly driven discrete nonlinear Schrödinger-type models”, Phys. Rev. E, 75:1 (2007)
Alidou Mohamadou, Ferdinand Fopa, Timoléon Crépin Kofané, “Modulational instability and spatial structures of the Ablowitz–Ladik equation”, Optics Communications, 266:2 (2006), 648
E.V. Doktorov, N.P. Matsuka, V.M. Rothos, NATO Science Series II: Mathematics, Physics and Chemistry, 153, Nonlinear Waves: Classical and Quantum Aspects, 2005, 489
J. Gómez-Gardeñes, F. Falo, L.M. Floría, “Mobile localization in nonlinear Schrödinger lattices”, Physics Letters A, 332:3-4 (2004), 213
E. V. Doktorov, N. P. Matsuka, V. M. Rothos, “Dynamics of the Ablowitz-Ladik soliton train”, Phys. Rev. E, 69:5 (2004)
E. V. Doktorov, N. P. Matsuka, V. M. Rothos, “Perturbation-induced radiation by the Ablowitz-Ladik soliton”, Phys. Rev. E, 68:6 (2003)
F.Kh Abdullaev, A.A Abdumalikov, B.A Umarov, “Autosoliton in Ablowitz–Ladik chain with linear damping and nonlinear amplification”, Physics Letters A, 305:6 (2002), 371
Dirk Hennig, “Energy transport in α-helical protein models: One-strand versus three-strand systems”, Phys. Rev. B, 65:17 (2002)
K Kundu, “A study of a new class of discrete nonlinear Schr dinger equations”, J. Phys. A: Math. Gen., 35:38 (2002), 8109
Oleksiy O. Vakhnenko, “Solitons on a zigzag-runged ladder lattice”, Phys. Rev. E, 64:6 (2001)
J. Garnier, “Propagation of solitons in a randomly perturbed Ablowitz-Ladik chain”, Phys. Rev. E, 63:2 (2001)
Yaroslav Zolotaryuk, J. Chris Eilbeck, “Analytical approach to the Davydov-Scott theory with on-site potential”, Phys. Rev. B, 63:5 (2001)
K. Kundu, “Perturbative study of classical Ablowitz-Ladik type soliton dynamics in relation to energy transport inα-helical proteins”, Phys. Rev. E, 61:5 (2000), 5839
Larissa Brizhik, Alexander Eremko, Leonor Cruzeiro-Hansson, Yulia Olkhovska, “Soliton dynamics and Peierls-Nabarro barrier in a discrete molecular chain”, Phys. Rev. B, 61:2 (2000), 1129
Oleksiy O. Vakhnenko, Michael J. Velgakis, “Multimode soliton dynamics in perturbed ladder lattices”, Phys. Rev. E, 63:1 (2000)
Dirk Hennig, “Solitonic energy transfer in a coupled exciton-vibron system”, Phys. Rev. E, 61:4 (2000), 4550
Oleksiy O. Vakhnenko, Michael J. Velgakis, “Transverse and longitudinal dynamics of nonlinear intramolecular excitations on multileg ladder lattices”, Phys. Rev. E, 61:6 (2000), 7110
D. Hennig, G.P. Tsironis, “Wave transmission in nonlinear lattices”, Physics Reports, 307:5-6 (1999), 333
F. Lederer, J. S. Aitchison, Optical Solitons: Theoretical Challenges and Industrial Perspectives, 1999, 349
Mark J. Ablowitz, Yasuhiro Ohta, A. David Trubatch, “On discretizations of the vector nonlinear Schrödinger equation”, Physics Letters A, 253:5-6 (1999), 287
S. Jiménez, V. V. Konotop, “Envelope solitons and companion modes in diatomic lattices”, Phys. Rev. B, 60:9 (1999), 6465
Oleksiy O. Vakhnenko, “Nonlinear model of intramolecular excitations on a multileg ladder lattice”, Phys. Rev. E, 60:3 (1999), R2492
K.Ø. Rasmussen, P.L. Christiansen, M. Johansson, Yu.B. Gaididei, S.F. Mingaleev, “Localized excitations in discrete nonlinear Schrödinger systems: Effects of nonlocal dispersive interactions and noise”, Physica D: Nonlinear Phenomena, 113:2-4 (1998), 134
Oleg M. Braun, Yuri S. Kivshar, “Nonlinear dynamics of the Frenkel–Kontorova model”, Physics Reports, 306:1-2 (1998), 1
K. Ø. Rasmussen, David Cai, A. R. Bishop, Niels Grønbech-Jensen, “Dynamics of nonlinear localized states on finite discrete chains”, Phys. Rev. E, 55:5 (1997), 6151
D. Hennig, K. Ø. Rasmussen, H. Gabriel, A. Bülow, “Solitonlike solutions of the generalized discrete nonlinear Schrödinger equation”, Phys. Rev. E, 54:5 (1996), 5788
V. V. Konotop, David Cai, M. Salerno, A. R. Bishop, Niels Grønbech-Jensen, “Interaction of a soliton with point impurities in an inhomogeneous, discrete nonlinear Schrödinger system”, Phys. Rev. E, 53:6 (1996), 6476
David Cai, A. R. Bishop, Niels Grønbech-Jensen, “Perturbation theories of a discrete, integrable nonlinear Schrödinger equation”, Phys. Rev. E, 53:4 (1996), 4131
Oleksiy O. Vakhnenko, Vyacheslav O. Vakhnenko, “Physically corrected Ablowitz-Ladik model and its application to the Peierls-Nabarro problem”, Physics Letters A, 196:5-6 (1995), 307
O. Bang, M. Peyrard, “High order breather solutions to a discrete nonlinear Klein-Gordon model”, Physica D: Nonlinear Phenomena, 81:1-2 (1995), 9
Oleksiy O. Vakhnenko, Vyacheslav O. Vakhnenko, “Physically corrected Ablowitz-Ladik model and its application to the Peierls-Nabarro problem”, Physics Letters A, 196:1-2 (1994), 307
Yuri S. Kivshar, David K. Campbell, “Peierls-Nabarro potential barrier for highly localized nonlinear modes”, Phys. Rev. E, 48:4 (1993), 3077
Ch. Claude, Yu. S. Kivshar, O. Kluth, K. H. Spatschek, “Moving localized modes in nonlinear lattices”, Phys. Rev. B, 47:21 (1993), 14228
A. V. Zolotaryuk, K. H. Spatschek, O. Kluth, “Nonlinear transport of vibrational energy in a random molecular chain”, Phys. Rev. B, 47:13 (1993), 7827
L. S. Brizhik, Yu. B. Gaididei, A. A. Vakhnenko, V. A. Vakhnenko, “Soliton Generation in Semi‐Infinite Molecular Chains”, Physica Status Solidi (b), 146:2 (1988), 605
