Dislocations of soliton lattices: experiment and theory

E.A. Kuznetsov^†^a, b
^aLebedev Physical Institute, Russian Academy of Sciences, Leninsky prosp. 53, Moscow, 119991, Russian Federation
^bLandau Institute for Theoretical Physics, Russian Academy of Sciences, ul. Kosygina 2, Moscow, 119334, Russian Federation

The results of recent experiments [1] on observing soliton lattices and their dislocations in vertical cylindrical channels filled with immiscible fluids with strongly different viscosities and but slightly different densities are discussed. The less viscous, lower-density fluid fills the central region of the cylinder. Injecting a light fluid from below generates nonlinear cnoidal waves at the interface between the fluids, which have the appearance of soliton lattices. Two types of lattice dislocations are observed, the interaction between which is elastic. This experimental study fully confirms the theory of cnoidal waves and their dislocations for the KDV equation, which was developed 50 years ago and published in JETP [2].

Correspondence should be addressed to
Keywords: breathers, dislocations, soliton, cnoidal wave, dressing procedure, KDV equation, Fermi—Pasta—Ulam recurrence
PACS: 05.45.Yv, 47.10.−g, 47.35.−i (all)
DOI: 10.3367/UFNe.2026.03.040111
URL: https://ufn.ru/en/articles/2026/6/f/
Citation: Kuznetsov E A "Dislocations of soliton lattices: experiment and theory" Phys. Usp. 69 615–620 (2026)

BibTexBibNote ® (generic)BibNote ® (RIS)MedlineRefWorks

Received: 25th, March 2026, accepted: 27th, March 2026

Оригинал: Кузнецов Е А «Дислокации солитонных решёток: эксперимент и теория» УФН 196 659–665 (2026); DOI: 10.3367/UFNr.2026.03.040111

References (25) Similar articles (20) ↓

P.N. Svirkunov, M.V. Kalashnik “Phase patterns of dispersive waves from moving localized sources” Phys. Usp. 57 80–91 (2014)
D.S. Agafontsev, E.A. Kuznetsov et al “Compressible vortex structures and their role in the onset of hydrodynamic turbulence” Phys. Usp. 65 189–208 (2022)
A.I. Musienko, L.I. Manevich “Classical mechanical analogs of relativistic effects” Phys. Usp. 47 797–820 (2004)
G.I. Broman, O.V. Rudenko “Submerged Landau jet: exact solutions, their meaning and application” Phys. Usp. 53 91–98 (2010)
V.P. Demutskii, R.V. Polovin “Conceptual problems in quantum mechanics” Sov. Phys. Usp. 35 (10) 857–896 (1992)
A.L. Zuev, K.G. Kostarev “Certain peculiarities of the solutocapillary convection” Phys. Usp. 51 1027–1045 (2008)
L.Kh. Ingel’ “’Anticonvection’” Phys. Usp. 40 741–745 (1997)
G. D’Abramo “On gravitational frequency shift derived from energy conservation” Phys. Usp. 68 87–93 (2025)
G.S. Golitsyn “A N Kolmogorov's 1934 paper is the basis for explaining the statistics of natural phenomena of the macrocosm” Phys. Usp. 67 80–90 (2024)
A.A. Abrashkin, E.N. Pelinovsky “Gerstner waves and their generalizations in hydrodynamics and geophysics” Phys. Usp. 65 453–467 (2022)
K.Yu. Todyshev “Measuring the inclusive cross section of e⁺e⁻ annihilation into hadrons in the pre-asymptotic energy range” Phys. Usp. 63 929–939 (2020)
G.V. Shpatakovskaya “Semiclassical method of analysis and estimation of the orbital binding energies in many-electron atoms and ions” Phys. Usp. 62 186–197 (2019)
A.A. Abrashkin, E.N. Pelinovsky “On the relation between Stokes drift and the Gerstner wave” Phys. Usp. 61 307–312 (2018)
G.B. Malykin, V.I. Pozdnyakova “Quadratic Sagnac effect — the influence of the gravitational potential of the Coriolis force on the phase difference between the arms of a rotating Michelson interferometer (an explanation of D C Miller's experimental results 1921—1926)” Phys. Usp. 58 398–406 (2015)
A.L. Buchachenko “Magnetoplasticity and the physics of earthquakes. Can a catastrophe be prevented?” Phys. Usp. 57 92–98 (2014)
A.D. Pryamikov, A.S. Biriukov “Excitation of cyclical Sommerfeld waves and Wood’s anomalies in plane wave scattering from a dielectric cylinder at oblique incidence” Phys. Usp. 56 813–822 (2013)
V.V. Shevchenko “Localization of a stationary electromagnetic field by a planar boundary of a metamaterial” Phys. Usp. 54 1131–1142 (2011)
P.S. Landa, D.I. Trubetskov, V.A. Gusev “Delusions versus reality in some physics problems: theory and experiment” Phys. Usp. 52 235–255 (2009)
L.A. Rivlin “Photons in a waveguide (some thought experiments)” Phys. Usp. 40 291–303 (1997)
A.V. Belinskii “Bell’s theorem for trichotomic observables” Phys. Usp. 40 305–316 (1997)

The list is formed automatically.