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Landau Institute for Theoretical Physics P.G. Demidov Yaroslavl State University Lebedev Physical Institute of the Russian Academy of Sciences Novosibirsk State Univeristy IT company “Tensor” IX International Scientiﬁc Conference “SOLITONS, COLLAPSES AND TURBULENCE: Achievements, Developments and Perspectives” (SCT-19) in honor of Vladimir Zakharov’s 80th birthday ABSTRACTS Yaroslavl, August 5–9, 2019 IX International Scientiﬁc Conference SOLITONS, COLLAPSES AND TURBULENCE Yaroslavl, August 5–9, 2019 ORGANIZERS Landau Institute for Theoretical Physics P.G. Demidov Yaroslavl State University Lebedev Physical Institute of the Russian Academy of Sciences Novosibirsk State Univeristy IT company “Tensor” PROGRAM COMMITTEE Alan C. NEWELL (Chairman), Mikhail P. FEDORUK, Vladimir V. LEBEDEV, Jens J. RASMUSSEN, Sergei K. TURITSYN ORGANIZING COMMITTEE Evgeny A. KUZNETSOV (Chairman), Alexandre V. MIKHAILOV (co-chairman), Аnna O. Tolbey (secretary), Alexandre I. DYACHENKO, Sergei A. IGONIN, Sotiris G. KONSTANTINOU-RIZOS, Pavel N. NESTEROV, Valery A. SOKOLOV УДК 530.145+532 ББК 22.314+22.253.3 С60 С60 Солитоны, коллапсы и турбулентность: достижения, развитие и перспективы: IX международная конференция в честь 80-летнего юбилея академика РАНВ. Е. Захарова : тези- сы докладов. – Ярославль : ЯрГУ ; Филигрань, 2019. – 138 с. – (5–9 августа 2019 г., г. Ярославль) ISBN 978-5-6042792-8-1 Ярославский государственный университет им. П. Г. Демидова проводит с 5 по 9 августа 2019 года в г. Ярославле международ- ную научную конференцию «Солитоны, коллапсы и турбулентность: достижения, развитие и перспективы». Данный сборник содержит тезисы докладов, представленных на конференцию. Тезисы докла- дов публикуются в авторской редакции. Конференция проводится в рамках государственного задания Министерства образования и науки РФ (проект № 1.13560.2019/13.1), при финансовой поддержке РФФИ (проект № 19-01-20094). УДК 530.145+532 ББК 22.314+22.253.3 ISBN 978-5-6042792-8-1 c ЯрГУ, 2019 CONTENTS Abdullaev F. Kh., Gammal A., Kumar R. K., Tomio L. Faraday waves and droplets in quasi-one-dimensional Bosegasmixture..................... 13 Aceves A. B. Recent trends in nonlinear optics and photonics: amathematicalmodelingperspective.......... 14 Agafonov S. I. Contact structure on Fano variety of quadric and con- servation laws of Hamiltonian PDEs ........... 14 Agafontsev D. S., Randoux S., Suret P. Generation of rogue waves from random waveﬁeld of high nonlinearity ..................... 14 Alekseev G. A. Einstein equations: solution-generating methods as ”co- ordinate” transformations in the solution space .... 17 Annenkov S. Y., Shrira V. I. Evolution of weakly nonlinear random wave ﬁelds: ki- neticequationsvstheZakharovequation........ 19 Badulin S. I., Zakharov V. E. The generalized Phillips spectrum and wind-wave dis- sipation.......................... 21 Bagderina Yu. Yu. Point equivalence of second-order odes to the Painlev´e equations......................... 22 Balakin A. A., Fraiman G. M., Skobelev S. A. Raman compression of laser pulses in wedge-shaped jet plasma........................... 25 Balakin A. A., Litvak A. G., Skobelev S. A. Coherent propagation and compression of laser pulses inopticalmulti-coreﬁber................. 26 4 CONTENTS Bogdanov L. V. Six-dimensional heavenly equation and related systems. Dressingschemeandthehierarchy........... 27 Bogdanov S. A., Redyuk A. A. Investigation of soliton communication lines ...... 27 Buchstaber V. M., Mikhailov A. V. Polynomial integrable Hamiltonian systems and sym- metricpowersofC2 .................... 28 Buryak A. Yu. Generalization of the Givental theory for the oriented WDVVequations..................... 30 Bychkov B. S. Polynomial graph invariants and linear hierarchies . 30 Calogero F. Algebraically solvable systems of nonlinear ordinary dif- ferentialequations.................... 31 Chabchoub A. Solitons and breathers: an environmental ﬂuid mechan- icsperspective....................... 31 Chang Jen-Hsu, Lin Chun-Yan, Lee Ray-Kuang Nonlinear dispersion with quantum oscillator ...... 32 Chen Jinbing, Pelinovsky Dmitry E. Rogue waves on the periodic and double-periodic back- ground........................... 33 Didenkulova E. G., Pelinovsky E. N., Talipova T. G., Didenkulov O. I. Peculiarities of the oscillating wave packets (breathers) interaction within the framework of the modiﬁed Ko- rteweg-deVriesequation................ 34 Dremov S. V., Kachulin D. I., Dyachenko A. I. Soliton interactions in the system of supercompact equa- tions for counter propagating 1d waves ......... 35 Dryuma V. S. On generalization of Taylor-Green vortex solution of theNavier-Stokessystemofequations.......... 35 Dudley John M., Genty Go¨ery, Mussot Arnaud, Chab- choub Amin, Dias Fr´ed´eric Rogue waves and analogies in optics and oceanography 38 5 CONTENTS Dyachenko A. I. Newintegralsofmotionforwaterwaves........ 39 Dzhamay A., Knizel A. Discrete Painlev´e equations in tiling problems ..... 39 Eﬁmov V. B., Orlova A. A. About vortex turbulence formation by a heat ﬂux in superﬂuid helium in a long capillary ........... 41 El Gennady, Congy Thibault, Hoefer Mark Wave-mean ﬂow interactions in dispersive hydrodynamics 42 Erokhin N. S., Mikhailovskaya L. A., Zolnikova N. N. Nonlinear generation of ﬂows of ultrarelativistic charged particles by electromagnetic waves in the space plasma 43 Falkovich G., Shavit M. No weak turbulence for old men ............. 44 Ferapontov E. V. Integrable Lagrangians and Picard modular forms . 45 Garbuzov F. E., Beltukov Y. M., Khusnutdinova K. R. Forced Boussinesq-type models for nonlinear strain waves in solid waveguides .................... 46 Garifullin R. N., Yamilov R. I. Aseriesofautonomousquadequations......... 47 Gelash A., Agafontsev D., Zakharov V., Randoux S., El G., Suret P. Stronglyinteractingsolitongas............. 49 Geogjaev V. V. On stability of Kolmogorov spectra for surface gravity waterwaves........................ 50 Gerdjikov V. S. On dressing factors and soliton solutions of 2-dimensional Todaﬁeldtheories.................... 51 Glyzin S. D., Kashchenko S. A., Tolbey A. O. Normal form of equations with nonlinearities of dislo- cationsandFermi–Pasta–Ulama............. 52 Glyzin S. D., Kolesov A. Yu. Diﬀusionchaosanditsinvariantcharacteristics.... 54 Grahovski G. G. On the derivative nonlinear Schr¨odinger equation re- latedtosymmetricspaces................ 56 6 CONTENTS Grinevich P. G., Santini P. M. Periodic NLS Cauchy problem for the rogue waves . 57 Habibullin I.T., Kusnetsova M. N. Classiﬁcation of integrable two-dimensional lattices via Lie-Rinehartalgebras................... 57 Hitzazis Iasonas The Fokas method and integrable nonlinear PDEs in time-dependentdomains................. 58 Ismailov K. K., Baizakov B. B., Abdullaev F. Kh., Salerno M. Bouncing of binary matter waves on reﬂecting barriers in the presence of gravity ................. 59 Kachulin D. I., Gelash A. A., Dyachenko A. I., Zakharov V. E. Interactions of coherent structures on the surface of deepwater......................... 61 Kalyakin L. A. Asymptotics of the dynamic bifurcation saddle-node . 62 Kamalian Kopae M., Vasylchenkova A., Shepelsky D., Prilepsky J., Turitsyn S. A ﬁbre-optic communication system using Inverse scat- tering transform based on solving a Riemann–Hilbert problem.......................... 63 Kamchatnov A. M. Dispersive shock wave theory for nonintegrable equations 66 Karabut E. A., Zhuravleva E. N. Reducing a free-boundary problem to the system of dif- ferentialequations.................... 67 Kashchenko A. A. Relaxation cycles in a model of two weakly coupled gen- eratorswithdelayedsign-changingfeedback...... 68 Kashchenko I. S. Spatially inhomogeneous solutions of the system with a deviationinspace..................... 70 Kassotakis P. Invariants in separated variables: Yang-Baxter, entwin- ing and transfer maps ................... 72 7 CONTENTS Khusnutdinova K. R. The eﬀects of the shear ﬂows on surface and internal ringwaves......................... 72 Kocharovsky Vl. V., Mishin A. V., Kocharovskaya E. R. Parametric origin of an intracavity soliton in a super- radiantlaserwithalow-Qcavity............ 74 Kocharovsky Vl. V., Mishin A. V., Nechaev A. A., Garasev M. A., Stepanov A. N., Kocharovsky V. V. A dense layer formation in an electrostatic collisionless shock wave during the expansion of a hot dense plasma intoarareﬁedone..................... 77 Kochurin E. A., Zubarev N. M. Wave turbulence and collapses at the free surface of a liquid dielectric in an external tangential electric ﬁeld . 79 Kolokolov I., Lebedev V. Structure of coherent vortices caused by the inverse cas- cade of 2D turbulence and related problems ...... 80 Konopelchenko B. G. Universal parabolic regularization of the gradient catas- trophes for the Burgers-Hopf equation and Jordan chain 81 Kontorovich V. M. Why is the microstructure of the main pulse and inter pulse of the pulsar in Crab so strikingly diﬀerent? . 81 Korotkevich A. O. Inverse cascade of gravity waves in the presence of con- densate: numerical results and analytical explanation . 83 Kruglikov B. S. Dispersionless Lax pairs: from Zakharov and Penrose tonowadays........................ 84 Kulikov A. N., Kulikov D. A. Landau–Hopf scenario of passage to turbulence can be realized.......................... 85 Kuznetsov E. A., Kagan M. Yu., Turlapov A. V. Expansion of the strongly interacting superﬂuid Fermi gas: symmetry and self-similar regimes ......... 87 8 CONTENTS Lebel Alexandre, Tikan Alexey, Kraych Adrien, Roberti Giacomo, Copie