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Hamiltonian formalism for nonlinear waves

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Landau Institute for Theoretical Physics, Russian Academy of Sciences, ul. Kosygina 2, Moscow, 119334, Russian Federation

The Hamiltonian description of hydrodynamic type systems in application to plasmas, hydrodynamics, and magnetohydrodynamics is reviewed with emphasis on the problem of introducing canonical variables. The relation to other Hamiltonian approaches, in particular natural-variable Poisson brackets, is pointed out. It is shown that the degeneracy of noncanonical Poisson brackets relates to a special type of symmetry, the relabeling transformations of fluid-particle Lagrangian markers, from which all known vorticity conservation theorems, such as Ertel’s, Cauchy’s, Kelvin’s, as well as vorticity frozenness and the topological Hopf invariant, are derived. The application of canonical variables to collisionless plasma kinetics is described. The Hamiltonian structure of Benney’s equations and of the Rossby wave equation is discussed. Davey-Stewartson’s equation is given the Hamiltonian form. A general method for treating weakly nonlinear waves is presented based on classical perturbation theory and the Hamiltonian reduction technique.

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Fulltext is also available at DOI: 10.1070/PU1997v040n11ABEH000304
PACS: 52.30.−q, 52.35.Ra, 52.55.Fa (all)
DOI: 10.1070/PU1997v040n11ABEH000304
URL: https://ufn.ru/en/articles/1997/11/a/
000071302300001
Citation: Zakharov V E, Kuznetsov E A "Hamiltonian formalism for nonlinear waves" Phys. Usp. 40 1087–1116 (1997)
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Îðèãèíàë: Çàõàðîâ Â Å, Êóçíåöîâ Å À «Ãàìèëüòîíîâñêèé ôîðìàëèçì äëÿ íåëèíåéíûõ âîëí» ÓÔÍ 167 1137–1167 (1997); DOI: 10.3367/UFNr.0167.199711a.1137

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  1. Gubarev Yu G, Kotelnikova M S Jour 166 36 (2024)
  2. Gurchenkov A A, Matveev I A Physics 6 426 (2024)
  3. Fukumoto Ya, Zou R 2024 (3) (2024)
  4. Abrashkin A A, Pelinovsky E N Theor Math Phys 215 599 (2023)
  5. Smirnov S, Podivilov E, Sturman B Photonics 10 640 (2023)
  6. Knyazev D V Comp. Contin. Mech. 16 150 (2023)
  7. Pezzutto P, Shrira V I J. Fluid Mech. 972 (2023)
  8. Sedletsky Yu V, Gandzha I S Proc. R. Soc. A. 479 (2277) (2023)
  9. Zheltikov A M Optics Communications 546 129766 (2023)
  10. (11TH INTERNATIONAL CONFERENCE ON MATHEMATICAL MODELING IN PHYSICAL SCIENCES) Vol. 11TH INTERNATIONAL CONFERENCE ON MATHEMATICAL MODELING IN PHYSICAL SCIENCESStudy of the stability for three-dimensional states of dynamic equilibrium of the electron Vlasov-Poisson gasYuriy G.GubarevYangLiu2872 (2023) p. 060024
  11. Markov Yu A, Markova M  A, Markov N  Yu Int. J. Mod. Phys. A 38 (02) (2023)
  12. Bibilova S A, Gubarev Y G Acta Appl Math 187 (1) (2023)
  13. Machado M G, Abanov A G, Ganeshan S SciPost Phys. 14 (5) (2023)
  14. Malkin V M, Fisch N J Phys. Rev. E 105 (4) (2022)
  15. Gönül Ş, Özemir C Chaos, Solitons & Fractals 165 112807 (2022)
  16. Markov Yu A, Markova M A, Markov N Yu Russ Phys J 64 2246 (2022)
  17. Abanov A  G, Wiegmann P  B Phys. Rev. Lett. 128 (5) (2022)
  18. Agafontsev D S, Kuznetsov E A et al Phys.-Usp. 65 189 (2022)
  19. Kochurin E A, Kuznetsov E A Jetp Lett. 116 863 (2022)
  20. Abrashkin A A, Pelinovsky E N Uspekhi Fizicheskikh Nauk 192 491 (2022)
  21. [Abrashkin A A, Pelinovsky E N Phys. Usp. 65 453 (2022)]
  22. Gönül Ş, Özemir C Eur. Phys. J. Plus 137 (10) (2022)
  23. Ludu A Nonlinear Waves and Solitons on Contours and Closed Surfaces Springer Series In Synergetics Chapter 9 (2022) p. 203
  24. Rumpf B, Lvov Yu V Fluids 7 122 (2022)
  25. Wiegmann P B, Abanov A G J. High Energ. Phys. 2022 (6) (2022)
  26. Webb G M, Anco S C et al J. Plasma Phys. 88 (4) (2022)
  27. Chong Ch L Physica D: Nonlinear Phenomena 433 133164 (2022)
  28. Sedletsky Yu V, Gandzha I S Phys. Rev. E 106 (6) (2022)
  29. Campolina C S, Mailybaev A A Nonlinearity 34 4684 (2021)
  30. Grosvenor K T, Hoyos C et al Phys. Rev. Research 3 (4) (2021)
  31. Abali B E, Klunker A et al Z Angew Math Mech 101 (9) (2021)
  32. Maltsev A Ya, Novikov S P J. Exp. Theor. Phys. 132 645 (2021)
  33. Grimberg G, Tassi E EPJ H 46 (1) (2021)
  34. Yahalom A Symmetry 13 1632 (2021)
  35. Spiller D, Brunk A et al J. Phys.: Condens. Matter 33 364001 (2021)
  36. Shashikanth B N Dynamically Coupled Rigid Body-Fluid Flow Systems Chapter 6 (2021) p. 133
  37. Yang Sh, Xiong Sh et al ACM Trans. Graph. 40 1 (2021)
  38. Pavlov V P, Sergeev V M, Shamin R V Theor Math Phys 208 926 (2021)
  39. Chong Ch L Journal Of Non-Newtonian Fluid Mechanics 292 104537 (2021)
  40. Vakhnenko O O JNMP 24 250 (2021)
  41. Kopiev V F, Chernyshev S A Acoust. Phys. 67 83 (2021)
  42. Yang Sh, Xiong Sh et al ACM Trans. Graph. 40 1 (2021)
  43. Gu Ya-Ju, Bulanov S V High Pow Laser Sci Eng 9 (2021)
  44. Gubarev Yu G, Sun S J. Phys.: Conf. Ser. 1730 012069 (2021)
  45. Yushkov V P Moscow Univ. Phys. 75 547 (2020)
  46. Kuznetsov E A, Mikhailov E A J. Exp. Theor. Phys. 131 496 (2020)
  47. Gubarev Yu G Continuum Mechanics, Applied Mathematics and Scientific Computing: Godunov’s Legacy Chapter 21 (2020) p. 161
  48. Sedletsky Yu V, Gandzha I  S Phys. Rev. E 102 (2) (2020)
  49. Zubarev N M, Zubareva O V J. Phys.: Conf. Ser. 1556 012014 (2020)
  50. Malkin V M, Fisch N J Phys. Rev. E 101 (2) (2020)
  51. Gürcan Ö D, Li Ya, Morel P Mathematics 8 530 (2020)
  52. Gerdjikov V S, Smirnov A O, Matveev V B Eur. Phys. J. Plus 135 (8) (2020)
  53. Krishnaswami G S, Phatak S S et al 10 (2) (2020)
  54. Abanov A G, Can T et al Phys. Rev. Fluids 5 (10) (2020)
  55. Cullen J, Ivanov R European Journal Of Mechanics - B/Fluids 84 325 (2020)
  56. Piterbarg L I Theor Math Phys 202 412 (2020)
  57. Xiong Sh, Yang Yu J. Fluid Mech. 895 (2020)
  58. Machon T Proc. R. Soc. A. 476 20190851 (2020)
  59. Zubareva O V, Zubarev N M, Bobrov K E J. Phys.: Conf. Ser. 1556 012015 (2020)
  60. Gültekin Ö, Gürcan Ö D Plasma Phys. Control. Fusion 62 025018 (2020)
  61. Gubarev Yu G Plasma Res. Express 1 045008 (2019)
  62. Dyachenko A I, Lushnikov P M, Zakharov V E J. Fluid Mech. 869 526 (2019)
  63. McKeever B F, Rodrigues D R et al Phys. Rev. B 99 (5) (2019)
  64. Yahalom A J. Phys.: Conf. Ser. 1416 012041 (2019)
  65. Khazanov E A, Mironov S Yu, Mourou G Uspekhi Fizicheskikh Nauk 189 1173 (2019) [Khazanov E A, Mironov S Yu, Mourou G Phys.-Usp. 62 1096 (2019)]
  66. Dullin H R, Meiss J D, Worthington J J. Phys. A: Math. Theor. 52 365501 (2019)
  67. Abrashkin A Deep Sea Research Part II: Topical Studies In Oceanography 160 3 (2019)
  68. Yahalom A J. Phys.: Conf. Ser. 1194 012113 (2019)
  69. Sato N, Yamada M J. Fluid Mech. 876 896 (2019)
  70. (MODERN TREATMENT OF SYMMETRIES, DIFFERENTIAL EQUATIONS AND APPLICATIONS (Symmetry 2019)) Vol. MODERN TREATMENT OF SYMMETRIES, DIFFERENTIAL EQUATIONS AND APPLICATIONS (Symmetry 2019)Conservation laws in magnetohydrodynamics and fluid dynamics: Lagrangian approachGary M.WebbStephen C.Anco2153 (2019) p. 020024
  71. Vedenyapin V V, Fimin N N, Chechetkin V M Comput. Math. And Math. Phys. 59 1816 (2019)
  72. Abanov A G, Monteiro G M Phys. Rev. Lett. 122 (15) (2019)
  73. Abrashkin A J. Math. Fluid Mech. 21 (2) (2019)
  74. Vakhnenko O O 59 (5) (2018)
  75. Kopiev V F, Chernyshev S A Acoust. Phys. 64 707 (2018)
  76. Shen L Q, Zhou L F et al Phys. Rev. B 97 (22) (2018)
  77. Webb G Lecture Notes In Physics Vol. Magnetohydrodynamics and Fluid Dynamics: Action Principles and Conservation LawsIntroduction946 Chapter 1 (2018) p. 1
  78. Buffoni B, Groves M D, Wahlén E Arch Rational Mech Anal 228 773 (2018)
  79. Krafft C, Volokitin A S 25 (10) (2018)
  80. Yahalom A Springer Proceedings In Mathematics & Statistics Vol. Quantum Theory and Symmetries with Lie Theory and Its Applications in Physics Volume 2Metage Symmetry Group of Non-barotropic Magnetohydrodynamics and the Conservation of Cross Helicity255 Chapter 30 (2018) p. 387
  81. Abrashkin A A, Pelinovsky E N Uspekhi Fizicheskikh Nauk 188 329 (2018)
  82. Yahalom A Fluid Dyn. Res. 50 011406 (2018)
  83. Webb G Lecture Notes In Physics Vol. Magnetohydrodynamics and Fluid Dynamics: Action Principles and Conservation LawsHelicity in Fluids and MHD946 Chapter 3 (2018) p. 21
  84. Webb G Lecture Notes In Physics Vol. Magnetohydrodynamics and Fluid Dynamics: Action Principles and Conservation LawsAdvected Invariants946 Chapter 5 (2018) p. 53
  85. Vedenyapin V V, Andreeva A A, Vorobyeva V V Dokl. Math. 97 283 (2018)
  86. Campolina C S, Mailybaev A A Phys. Rev. Lett. 121 (6) (2018)
  87. Vakhnenko O O Lett Math Phys 108 1807 (2018)
  88. Webb G Lecture Notes In Physics Vol. Magnetohydrodynamics and Fluid Dynamics: Action Principles and Conservation LawsHamiltonian Approach946 Chapter 8 (2018) p. 137
  89. Vedenyapin V V, Kazakova T S et al Dokl. Math. 97 240 (2018)
  90. Webb G Lecture Notes In Physics Vol. Magnetohydrodynamics and Fluid Dynamics: Action Principles and Conservation LawsMulti-Symplectic Clebsch Approach946 Chapter 9 (2018) p. 167
  91. Nishiyama S, da Providência J Int. J. Mod. Phys. E 26 1750020 (2017)
  92. Besse N, Frisch U J. Fluid Mech. 825 412 (2017)
  93. Benilov E S, Benilov M S Phys. Rev. E 96 (4) (2017)
  94. Yahalom A Geophysical & Astrophysical Fluid Dynamics 111 131 (2017)
  95. Banerjee D, Souslov A et al Nat Commun 8 (1) (2017)
  96. Vakhnenko O O Applied Mathematics Letters 64 81 (2017)
  97. Christov I C, Kress T, Saxena A Int. J. Mod. Phys. B 31 1742008 (2017)
  98. Chern A, Knöppel F et al ACM Trans. Graph. 36 1 (2017)
  99. Webb G M, Anco S C J. Phys. A: Math. Theor. 50 255501 (2017)
  100. Kuznetsov E A Jetp Lett. 105 125 (2017)
  101. Dutykh D, Clamond D et al Math. Model. Nat. Phenom. 12 23 (2017)
  102. Miloshevich G, Lingam M, Morrison P J New J. Phys. 19 015007 (2017)
  103. Vakhnenko O O Ukr. J. Phys. 62 271 (2017)
  104. Gelash A A, L’vov V S, Zakharov V E J. Fluid Mech. 831 128 (2017)
  105. Horikis T P, Frantzeskakis D J Phys. Rev. Lett. 118 (24) (2017)
  106. Camassa R, Falqui G, Ortenzi G Nonlinearity 30 466 (2017)
  107. Sen A Fluids 2 28 (2017)
  108. Romanova N N, Chkhetiani O G, Yakushkin I G J. Exp. Theor. Phys. 122 902 (2016)
  109. Cherubini Ch, Filippi S Commun. Comput. Phys. 19 758 (2016)
  110. Ludu A Boundaries of a Complex World Springer Series In Synergetics Chapter 9 (2016) p. 245
  111. Gu Y J, Klimo O et al Phys. Rev. E 93 (1) (2016)
  112. Grebenev V N, Oberlack M et al 57 (10) (2016)
  113. Webb G M, Anco S C J. Phys. A: Math. Theor. 49 075501 (2016)
  114. Matsuno Y Proc. R. Soc. A. 472 20160127 (2016)
  115. Amiranashvili Sh Lecture Notes In Physics Vol. New Approaches to Nonlinear WavesHamiltonian Framework for Short Optical Pulses908 Chapter 6 (2016) p. 153
  116. Onorato M, Baronio F et al Lecture Notes In Physics Vol. Rogue and Shock Waves in Nonlinear Dispersive MediaHydrodynamic and Optical Waves: A Common Approach for Unidimensional Propagation926 Chapter 1 (2016) p. 1
  117. Vakhnenko O O 57 (11) (2016)
  118. Ludu A Boundaries of a Complex World Springer Series In Synergetics Chapter 1 (2016) p. 3
  119. Hall M J W, Reginatto M Fundamental Theories Of Physics Vol. Ensembles on Configuration SpaceIntroduction184 Chapter 1 (2016) p. 3
  120. Yahalom A J. Plasma Phys. 82 (2) (2016)
  121. Gu Y J, Yu Q et al High Pow Laser Sci Eng 4 (2016)
  122. Clamond D, Dutykh D Lecture Notes In Physics Vol. New Approaches to Nonlinear WavesModeling Water Waves Beyond Perturbations908 Chapter 7 (2016) p. 197
  123. Webb G M, McKenzie J F, Zank G P J. Plasma Phys. 81 (6) (2015)
  124. Moroz S, Hoyos C Phys. Rev. B 91 (6) (2015)
  125. Gürcan Ö D, Diamond P H J. Phys. A: Math. Theor. 48 293001 (2015)
  126. Yushkov V P Moscow Univ. Phys. 70 217 (2015)
  127. Webb G M 56 (5) (2015)
  128. Kalashnikova A M, Kimel A V, Pisarev R V Uspekhi Fizicheskikh Nauk 185 1064 (2015) [Kalashnikova A M, Kimel A V, Pisarev R V Phys.-Usp. 58 969 (2015)]
  129. (Research Using Extreme Light: Entering New Frontiers with Petawatt-Class Lasers II) Vol. Research Using Extreme Light: Entering New Frontiers with Petawatt-Class Lasers IIMagnetic reconnection research with petawatt-class lasersGeorgKornLuis O.SilvaYanjunGuOndřejKlimoDeepakKumarYueLiuSushilSinghSergei V.BulanovTimur Z.EsirkepovStefanWeberGeorgKorn9515 (2015) p. 95151H
  130. Gu Y J, Klimo O et al 22 (10) (2015)
  131. Aseeva N V, Gromov E M, Tyutin V V Radiophys Quantum El 58 209 (2015)
  132. Monteiro G M, Abanov A G, Nair V  P Phys. Rev. D 91 (12) (2015)
  133. Ignatov A M Plasma Phys. Rep. 41 783 (2015)
  134. Tanehashi K, Yoshida Z J. Phys. A: Math. Theor. 48 495501 (2015)
  135. Webb G M, Dasgupta B et al J. Phys. A: Math. Theor. 47 095502 (2014)
  136. Webb G M, McKenzie J F, Zank G P J. Plasma Phys. 80 707 (2014)
  137. Camassa R, Chen S et al J. Fluid Mech. 743 534 (2014)
  138. Camassa R, Falqui G et al J. Phys.: Conf. Ser. 482 012006 (2014)
  139. Perin M, Chandre C et al Annals Of Physics 348 50 (2014)
  140. Prakash Ja, Lavrenteva O M, Nir A 26 (7) (2014)
  141. Zubarev N M, Kuznetsov E A J. Exp. Theor. Phys. 119 169 (2014)
  142. Frewer M, Oberlack M, Grebenev V N Math Phys Anal Geom 17 3 (2014)
  143. Webb G M, Dasgupta B et al J. Phys. A: Math. Theor. 47 095501 (2014)
  144. Ruban V P Jetp Lett. 99 124 (2014)
  145. Turchetti G, Sinigardi S, Londrillo P Eur. Phys. J. D 68 (12) (2014)
  146. Frisch U, Villone B EPJ H 39 325 (2014)
  147. Kovriguine D A Arch Appl Mech 84 159 (2014)
  148. Chandre C, de Guillebon L et al J. Phys. A: Math. Theor. 46 125203 (2013)
  149. Dvornikov M J. Phys. A: Math. Theor. 46 045501 (2013)
  150. Lyutikov M Phys. Rev. E 88 (5) (2013)
  151. Camassa R, Chen S et al J. Fluid Mech. 726 404 (2013)
  152. Sultana Sh, Rahman Z OJFD 03 75 (2013)
  153. Makarov V A, Petnikova V M et al Phys. Wave Phen. 21 264 (2013)
  154. Abanov A G J. Phys. A: Math. Theor. 46 292001 (2013)
  155. Clamond D, Dutykh D Physica D: Nonlinear Phenomena 241 25 (2012)
  156. Chandre C, Morrison P J, Tassi E Physics Letters A 376 737 (2012)
  157. Kulkarni M, Abanov A G Phys. Rev. A 86 (3) (2012)
  158. Dvornikov M Found Phys 42 1469 (2012)
  159. Lakhturov I, Adytia D, van Groesen E Wave Motion 49 309 (2012)
  160. Gibbon J D, Holm D D Mathematical Aspects of Fluid Mechanics 1 9 (2012) p. 201
  161. Zakharov V E, Kuznetsov E A Uspekhi Fizicheskikh Nauk 182 569 (2012) [Zakharov V E, Kuznetsov E A Phys.-Usp. 55 535 (2012)]
  162. Webb G M, Hu Q et al J. Phys. A: Math. Theor. 45 025203 (2012)
  163. de Guillebon L, Chandre C Physics Letters A 376 3172 (2012)
  164. Sokolov V V, Fotov K N, Eminov P A Dokl. Phys. 56 467 (2011)
  165. Nazarenko S V Lecture Notes In Physics Vol. Wave TurbulenceWave Turbulence Formalism825 Chapter 6 (2011) p. 67
  166. Rassmusen A R, Sørensen M P et al Acta Appl Math 115 43 (2011)
  167. Kuznetsov E A, Dias F Physics Reports 507 43 (2011)
  168. Felderhof B U, Sokolov V V, Éminov P A 135 (14) (2011)
  169. Amiranashvili Sh, Demircan A Advances In Optical Technologies 2011 1 (2011)
  170. Nazarenko S Lecture Notes In Physics Vol. Wave TurbulenceMagneto-Hydrodynamic Turbulence825 Chapter 14 (2011) p. 209
  171. Sokolov V V, Fotov K N, Eminov P A Russ Phys J 53 732 (2010)
  172. Brio M, Webb G M, Zakharian A R Mathematics In Science And Engineering Vol. Numerical Time-Dependent Partial Differential Equations for Scientists and EngineersProblems with Multiple Temporal and Spatial Scales213 (2010) p. 175
  173. Amiranashvili Sh, Demircan A Phys. Rev. A 82 (1) (2010)
  174. Rasmussen A R, Sørensen M P et al Mathematics In Industry Vol. Progress in Industrial Mathematics at ECMI 2008Analytical and Numerical Modelling of Thermoviscous Shocks and Their Interactions in Nonlinear Fluids Including Dissipation15 Chapter 159 (2010) p. 997
  175. Ruban V P J. Exp. Theor. Phys. 111 776 (2010)
  176. Mathematics In Science And Engineering Vol. Numerical Time-Dependent Partial Differential Equations for Scientists and EngineersBibliography213 (2010) p. 273
  177. Zubarev N M, Zubareva O V Phys. Rev. E 82 (4) (2010)
  178. Webb G M, Hu Q et al J. Geophys. Res. 115 (A10) (2010)
  179. Yahalom A Europhys. Lett. 89 34005 (2010)
  180. Nakamura T, Bulanov S V et al Phys. Rev. Lett. 105 (13) (2010)
  181. Zubarev N M Jetp Lett. 89 271 (2009)
  182. Sokolov V V, Tolmachev V V, Éminov P A Dokl. Phys. 54 488 (2009)
  183. Dünweg B, Ladd A J C Advanced Computer Simulation Approaches for Soft Matter Sciences III Chapter 2 (2009) p. 89
  184. Kharif Ch, Pelinovsky E, Slunyaev A Rogue Waves in the Ocean Advances In Geophysical And Environmental Mechanics And Mathematics Chapter 3 (2009) p. 33
  185. Levich E Old And New Concepts Of Physics 6 239 (2009)
  186. Petnikova V M, Shuvalov V V Phys. Rev. E 79 (2) (2009)
  187. Gordeev A V, Losseva T V Plasma Phys. Rep. 35 118 (2009)
  188. Kovalevskii M Yu, Kovalevsky M Yu i dr Teor. Mat. Fiz. 158 277 (2009) [Kovalevskii M Yu, Matskevich V T, Razumnyi A Ya Theor Math Phys 158 233 (2009)]
  189. Jin-Zhang P, Hong Ya, Yi T Chinese Phys. B 18 2364 (2009)
  190. Kalashnikova A M, Kimel A V et al Phys. Rev. B 78 (10) (2008)
  191. Petnikova V M, Shuvalov V V Quantum Electron. 38 1135 (2008)
  192. YAHALOM ASHER, LYNDEN-BELL DONALD J. Fluid Mech. 607 235 (2008)
  193. Maksimov A O J. Exp. Theor. Phys. 106 355 (2008)
  194. Zubarev N M J. Exp. Theor. Phys. 107 668 (2008)
  195. Radu E, Volkov M S Physics Reports 468 101 (2008)
  196. Shivamoggi B K, van Heijst G J F Physics Letters A 372 5688 (2008)
  197. Gibbon J D Physica D: Nonlinear Phenomena 237 1894 (2008)
  198. Romanova N N Izv. Atmos. Ocean. Phys. 44 53 (2008)
  199. KUZNETSOV E A J. Fluid Mech. 600 167 (2008)
  200. Romanova N N, Yakushkin I G Izv. Atmos. Ocean. Phys. 43 533 (2007)
  201. Petnikova V M, Shuvalov V V Phys. Rev. E 76 (4) (2007)
  202. Agafontsev D S, Dias F, Kuznetsov E A Physica D: Nonlinear Phenomena 225 153 (2007)
  203. Gutshabash E Sh J Math Sci 143 2765 (2007)
  204. Gibbon Dzh, Gibbon J Usp. Mat. Nauk 62 47 (2007)
  205. Sedletsky Yu V Jetp Lett. 86 502 (2007)
  206. Kuznetsov E A JNMP 13 64 (2006)
  207. Morrison P J Encyclopedia of Mathematical Physics (2006) p. 593
  208. Kalashnik M V, Ingel L Kh J. Exp. Theor. Phys. 103 141 (2006)
  209. Sedletsky Yu V J. Phys. A: Math. Gen. 39 L529 (2006)
  210. Protogenov A P Uspekhi Fizicheskikh Nauk 176 689 (2006)
  211. Agafontsev D S, Dias F, Kuznetsov E A Jetp Lett. 83 201 (2006)
  212. Belmont G, Sahraoui F, Rezeau L Advances In Space Research 37 1503 (2006)
  213. Sedletsky Yu V Physics Letters A 343 293 (2005)
  214. Eshraghi H, Abedini Y 46 (4) (2005)
  215. Dolzhanskii F V Uspekhi Fizicheskikh Nauk 175 1257 (2005)
  216. Ignatov A M Plasma Phys. Rep. 30 44 (2004)
  217. Kats A V Phys. Rev. E 69 (4) (2004)
  218. Khomeriki R, Tkeshelashvili L J. Opt. Soc. Am. B 21 2175 (2004)
  219. Ruban V P, Senchenko S L Phys. Scr. 69 227 (2004)
  220. Kuznetsov E A, Passot T, Sulem P L 11 1410 (2004)
  221. Ruban V P Phys. Rev. E 70 (6) (2004)
  222. Prix R Phys. Rev. D 69 (4) (2004)
  223. Dobrokhotov S Yu, Dobrokhotov S Yu i dr Teor. Mat. Fiz. 139 62 (2004)
  224. Hall M J W J. Phys. A: Math. Gen. 37 7799 (2004)
  225. Isaev L S, Protogenov A P J. Exp. Theor. Phys. 96 1140 (2003)
  226. Ruban V P Phys. Rev. E 67 (6) (2003)
  227. Kats A V Jetp Lett. 77 657 (2003)
  228. Dellar P J 10 581 (2003)
  229. Ruban V P Phys. Rev. E 68 (4) (2003)
  230. Sedletsky Yu V J. Exp. Theor. Phys. 97 180 (2003)
  231. Sahraoui F, Belmont G, Rezeau L 10 1325 (2003)
  232. Annenkov S Yu, Romanova N N Dokl. Phys. 48 441 (2003)
  233. Ruban V P, Juul R J Phys. Rev. E 68 (5) (2003)
  234. Garnier J, Cherfils-Clérouin C, Holstein P -A Phys. Rev. E 68 (3) (2003)
  235. Holm D D Geometry, Mechanics, and Dynamics Chapter 4 (2002) p. 169
  236. Protogenov A P, Verbus V A Jetp Lett. 76 53 (2002)
  237. Ruban V P Phys. Rev. E 65 (4) (2002)
  238. Dellar P J 9 1130 (2002)
  239. Ruban V P, Podolsky D I, Rasmussen J J Phys. Rev. E 63 (5) (2001)
  240. Romanova N N, Yakushkin I G Dokl. Phys. 46 742 (2001)
  241. Ruban V P, Podolsky D I Phys. Rev. D 64 (4) (2001)
  242. Ruban V P Phys. Rev. E 64 (3) (2001)
  243. Zubarev N M, Zubareva O V Tech. Phys. 46 806 (2001)
  244. Kats A V Physica D: Nonlinear Phenomena 152-153 459 (2001)
  245. Bogdanov A V, Stankova E N Lecture Notes In Computer Science Vol. High-Performance Computing and NetworkingThe Use of Intrinsic Properties of Physical System for Derivation of High-Performance Computational Algorithms2110 Chapter 21 (2001) p. 204
  246. Kuznetsov E A J. Exp. Theor. Phys. 93 1052 (2001)
  247. Zaiko Yu N Tech. Phys. Lett. 26 889 (2000)
  248. Dobrokhotov S Yu, Dobrokhotov S Yu Teor. Mat. Fiz. 125 491 (2000)
  249. Kuznetsov E A, Ruban V P Phys. Rev. E 61 831 (2000)
  250. Graham C R, Henyey F S 12 744 (2000)
  251. Ruban V P Phys. Rev. D 62 (12) (2000)
  252. V S D Physica D: Nonlinear Phenomena 139 186 (2000)
  253. Kuznetsov E A, Zakharov V E Lecture Notes In Physics Vol. Nonlinear Science at the Dawn of the 21st CenturyNonlinear Coherent Phenomena in Continuous Media542 Chapter 1 (2000) p. 3
  254. Kuznetsov E A, Ruban V P J. Exp. Theor. Phys. 91 775 (2000)
  255. Son D T Phys. Rev. Lett. 84 3771 (2000)
  256. Ruban V P Phys. Rev. E 62 4950 (2000)
  257. Rylov Yu A 40 256 (1999)
  258. Yoshikawa T, Balk A M Physics Letters A 251 184 (1999)
  259. Kuznetsov E A, Ruban V P J. Exp. Theor. Phys. 88 492 (1999)
  260. Kuznetsov E A J. Exp. Theor. Phys. 89 163 (1999)
  261. Kuznetsov E A Optical Solitons: Theoretical Challenges and Industrial Perspectives Chapter 3 (1999) p. 31
  262. Ruban V P J. Exp. Theor. Phys. 89 299 (1999)
  263. Kuznetsov E A, Ruban V P Lecture Notes In Physics Vol. Nonlinear MHD Waves and TurbulenceDynamics of Vortex and Magnetic Lines in Ideal Hydrodynamics and MHD536 Chapter 14 (1999) p. 346
  264. Kuznetsov E A, Ruban V P Jetp Lett. 67 1076 (1998)
  265. Berning M, Rubenchik A M 10 1564 (1998)
  266. Vol. MMET Conference Proceedings. 1998 International Conference on Mathematical Methods in Electromagnetic Theory. MMET 98 (Cat. No.98EX114)Hamiltonian approach to the problem of wave collapseV.V.Gushchin1 (1998) p. 266
  267. Zakharov V E, Kuznetsov E A J. Exp. Theor. Phys. 86 1035 (1998)
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