Issues

 / 

2016

 / 

May

  

Reviews of topical problems


Discrete breathers in crystals

 a, b,  b,  c, b,  d
a Tomsk State University, prosp. Lenina 36, Tomsk, 634050, Russian Federation
b Institute for Metals Superplasticity Problems of RAS, Khalturina st. 39, Ufa, 450001, Russian Federation
c Mikheev Institute of Metal Physics, Ural Division of the Russian Academy of Sciences, S Kovalevskoi str. 18, Ekaterinburg, 620108, Russian Federation
d Instituto Pluridisciplinar, Universidad Complutense, Paseo Juan XXIII, 1, Madrid, 28040, Spain

It is well known that periodic discrete defect-containing systems, in addition to traveling waves, support vibrational defect-localized modes. It turned out that if a periodic discrete system is nonlinear, it can support spatially localized vibrational modes as exact solutions even in the absence of defects. Since the nodes of the system are all on equal footing, it is only through the special choice of initial conditions that a group of nodes can be found on which such a mode, called a discrete breather (DB), will be excited. The DB frequency must be outside the frequency range of the small-amplitude traveling waves. Not resonating with and expending no energy on the excitation of traveling waves, a DB can theoretically conserve its vibrational energy forever provided no thermal vibrations or other perturbations are present. Crystals are nonlinear discrete systems, and the discovery in them of DBs was only a matter of time. Experimental studies of DBs encounter major technical difficulties, leaving atomistic computer simulations as the primary investigation tool. Despite the definitive evidence for the existence of DBs in crystals, their role in solid state physics still remains unclear. This review addresses some of the problems that are specific to real crystal physics and which went undiscussed in the classical literature on DBs. In particular, the interaction of a moving DB with lattice defects is examined, how elastic lattice deformations influence the properties of DBs and the possibility of their existence is discussed, recent studies of the effect of nonlinear lattice perturbations on the crystal electron subsystem are presented, etc.

Fulltext is available at IOP
Keywords: crystal lattice, nonlinear oscillations, discrete breather, crystal lattice defect
PACS: 05.45.−a, 05.45.Yv, 63.20.−e (all)
DOI: 10.3367/UFNe.2016.02.037729
URL: https://ufn.ru/en/articles/2016/5/b/
Citation: Dmitriev S V, Korznikova E A, Baimova J A, Velarde M G "Discrete breathers in crystals" Phys. Usp. 59 446–461 (2016)
BibTexBibNote ® (generic)BibNote ® (RIS)MedlineRefWorks

Received: 27th, July 2015, revised: 30th, January 2016, 9th, February 2016

Оригинал: Дмитриев С В, Корзникова Е А, Баимова Ю А, Веларде М Г «Дискретные бризеры в кристаллах» УФН 186 471–488 (2016); DOI: 10.3367/UFNr.2016.02.037729

References (241) ↓ Cited by (67) Similar articles (20)

  1. Kosevich A M, Kovalev A S Zh. Eksp. Teor. Fiz. 67 1793 (1974); Kosevich A M, Kovalev A S Sov. Phys. JETP 40 891 (1975)
  2. Dolgov A S Fiz. Tverd. Tela 28 1641 (1986); Dolgov A S Sov. Phys. Solid State 28 907 (1986)
  3. Sievers A J, Takeno S Phys. Rev. Lett. 61 970 (1988)
  4. Page J B Phys. Rev. B 41 7835 (1990)
  5. Lifshits I M Zh. Eksp. Teor. Fiz. 12 156 (1942)
  6. Lifshitz I M Nuovo Cimento Suppl. 3 716 (1956)
  7. Lifshits I M Usp. Fiz. Nauk 83 617 (1964); Lifshitz I M Sov. Phys. Usp. 7 549 (1965)
  8. Lifshitz I M, Kosevich A M Rep. Prog. Phys. 29 217 (1966)
  9. Lifshits I M Izbrannye Trudy. Fizika Real’nykh Kristallov i Neuporyadochennykh Sistem (M.: Nauka, 1987)
  10. Ovchinnikov A A Zh. Eksp. Teor. Fiz. 57 263 (1969); Ovchinnikov A A Sov. Phys. JETP 30 147 (1970)
  11. Ovchinnikov A A, Erikhman N S Usp. Fiz. Nauk 138 289 (1982); Ovchinnikov A A, Erikhman N S Sov. Phys. Usp. 25 738 (1982)
  12. MacKay R S, Aubry S Nonlinearity 7 1623 (1994)
  13. Bambusi D Nonlinearity 9 433 (1996)
  14. Livi R, Spicci M, MacKay R S Nonlinearity 10 1421 (1997)
  15. Alfimov G L, Brazhnyi V A, Konotop V V Physica D 194 127 (2004)
  16. Yoshimura K Proc. of the Intern. Symp. on Nonlinear Theory and its Applications, NOLTA2015, Hong Kong, China, December 1 - 4, 2015 p. 902
  17. Yoshimura K AIP Conf. Proc. 1474 59 (2012)
  18. Adler V E Teor. Mat. Fiz. 181 (2) 276 (2014); Adler V E Theor. Math. Phys. 181 1367 (2014)
  19. Adler V E, Bobenko A I, Suris Yu B Funkts. Analiz Ego Pril. 43 3 (2009); Adler V E, Bobenko A I, Suris Yu B Funct. Anal. Appl. 43 3 (2009)
  20. Suris Yu B Encyclopedia Of Mathematical Physics Vol. 5 (Eds J-P Francoise, G L Naber, S T Tsou) (Amsterdam: Elsevier, 2006) p. 235
  21. Suris Yu B Lecture Notes Phys. 644 111 (2004)
  22. Adler V E, Bobenko A I, Suris Yu B Commun. Math. Phys. 233 513 (2003)
  23. Dauxois T, Peyrard M, Ruffo S Eur. J. Phys. 26 S3 (2005)
  24. Morse P M Phys. Rev. 34 57 (1929)
  25. Braun O M, Kivshar’ Yu S Model’ Frenkelya - Kontorovoi. Kontseptsii, Metody, Prilozheniya (M.: Fizmatlit, 2008)
  26. Kevrekidis P G The Discrete Nonlinear Schrödinger Equation. Mathematical Analysis, Numerical Computations And Physical Perspectives (Springer Tracts in Modern Physics) Vol. 232 (Berlin: Springer, 2009)
  27. Salerno M Phys. Rev. A 46 6856 (1992)
  28. Ablowitz M J, Ladik J F J. Math. Phys. 16 598 (1975)
  29. Dutta O et al. Rep. Prog. Phys. 78 066001 (2015)
  30. Eisenberg H S et al. Phys. Rev. Lett. 81 3383 (1998)
  31. Christodoulides D N, Efremidis N K Opt. Lett. 27 568 (2002)
  32. Fleischer J W et al. Nature 422 147 (2003)
  33. Eiermann B et al. Phys. Rev. Lett. 92 230401 (2004)
  34. Trías E, Mazo J J, Orlando T P Phys. Rev. Lett. 84 741 (2000)
  35. Binder P et al. Phys. Rev. Lett. 84 745 (2000)
  36. Mazo J J, Orlando T P Chaos 13 733 (2003)
  37. Palmero F et al. Phys. Rev. E 84 026605 (2011)
  38. English L Q et al. Phys. Rev. Lett. 108 084101 (2012)
  39. Sato M et al. Phys. Rev. Lett. 90 044102 (2003)
  40. Wiersig J, Flach S, Ahn K H Appl. Phys. Lett. 93 222110 (2008)
  41. Sato M et al. Phys. Rev. E 87 012920 (2013)
  42. Sato M et al. Phys. Rev. Lett. 107 234101 (2011)
  43. Sato M et al. Chaos 25 013103 (2015)
  44. Flach S, Willis C R Phys. Rep. 295 181 (1998)
  45. Flach S, Gorbach A V Phys. Rep. 467 1 (2008)
  46. Swanson B I et al. Phys. Rev. Lett. 82 3288 (1999)
  47. Voulgarakis N K et al. Phys. Rev. B 64 020301(R) (2001)
  48. Kalosakas G, Bishop A R, Shreve A P Phys. Rev. B 66 094303 (2002)
  49. Campbell D K, Flach S, Kivshar Yu S Phys. Today 57 (1) 43 (2004)
  50. Manley M E et al. Phys. Rev. B 77 214305 (2008)
  51. Manley M E et al. Phys. Rev. Lett. 96 125501 (2006)
  52. Manley M E et al. Phys. Rev. B 79 134304 (2009)
  53. Kempa M et al. J. Phys. Condens. Matter. 25 055403 (2013)
  54. Sievers A J et al. Phys. Rev. B 88 104305 (2013)
  55. Archilla J F R et al. Physica D 297 56 (2015)
  56. Kiselev S A, Sievers A J Phys. Rev. B 55 5755 (1997)
  57. Khadeeva L Z, Dmitriev S V Phys. Rev. B 81 214306 (2010)
  58. Kirsanova A A, Baimova Yu A, Dmitriev S V Pis’ma ZhTF 38 (14) 72 (2012); Kistanov A A, Baimova Yu A, Dmitriev S V Tech. Phys. Lett. 38 676 (2012)
  59. Voulgarakis N K et al. Phys. Rev. B 69 113201 (2004)
  60. Yamayose Y et al. Europhys. Lett. 80 40008 (2007)
  61. Shimada T, Shirasaki D, Kitamura T Phys. Rev. B 81 035401 (2010)
  62. Shimada T et al. Physica D 239 407 (2010)
  63. Kinoshita Y et al. Phys. Rev. B 77 024307 (2008)
  64. Doi Y, Nakatani A J. Sol. Mech. Mater. Eng. 6 71 (2012)
  65. Haas M et al. Phys. Rev. B 84 144303 (2011)
  66. Hizhnyakov V et al. Phys. Scripta 89 044003 (2014)
  67. Savin A V, Kivshar Yu S Phys. Rev. B 85 125427 (2012)
  68. Khadeeva L Z, Dmitriev S V, Kivshar’ Yu S Pis’ma ZhETF 94 580 (2011); Khadeeva L Z, Dmitriev S V, Kivshar Yu S JETP Lett. 94 539 (2011)
  69. Baimova J A, Dmitriev S V, Zhou K Europhys. Lett. 100 36005 (2012)
  70. Korznikova E A, Baimova J A, Dmitriev S V Europhys. Lett. 102 60004 (2013)
  71. Korznikova E A i dr. Pis’ma ZhETF 96 238 (2012); Korznikova E A et al. JETP Lett. 96 222 (2012)
  72. Liu B et al. J. Phys. D 46 305302 (2013)
  73. Chechin G M et al. Phys. Rev. B 90 045432 (2014)
  74. Medvedev N N i dr. Pis’ma Materialakh 3 (1) 34 (2013)
  75. Zakharov P V i dr. Fundamental’nye Problemy Sovremennogo Materialovedeniya 11 (2) 260 (2014)
  76. Medvedev N N, Starostenkov M D, Manley M E J. Appl. Phys. 114 213506 (2013)
  77. Medvedev N N i dr. Izv. Vuzov. Fizika (3) 92 (2014); Medvedev N N et al. Russ. Phys. J. 57 387 (2014)
  78. Dmitriev S V i dr. Fiz. Tverd. Tela 52 1398 (2010); Dmitriev S V et al. Phys. Solid State 52 1499 (2010)
  79. Zakharov P V i dr. Fundamental’nye Problemy Sovremennogo Materialovedeniya 11 (4) 533 (2014)
  80. Zakharov P V i dr. Zh. Eksp. Teor. Fiz. 148 252 (2015); Zakharov P V et al. JETP 121 217 (2015)
  81. Medvedev N N i dr. Pis’ma ZhTF 41 (20) 50 (2015); Medvedev N N et al. Tech. Phys. Lett. 41 994 (2015)
  82. Zakharov P V i dr. Fundamental’nye Problemy Sovremennogo Materialovedeniya 12 (2) 146 (2015)
  83. Tsaregorodtsev A I i dr. Fiz. Met. Metalloved. 58 (2) 336 (1994)
  84. Hizhnyakov V, Klopov M, Shelkan A Phys. Lett. A 380 1075 (2016)
  85. Baimova Yu A i dr. Zh. Eksp. Teor. Fiz. 149 1005 (2016); Baimova J A et al. JETP 122 (5) (2016)
  86. Baimova J A et al. Rev. Adv. Mater. Sci. 42 68 (2015)
  87. Murzaev R T et al. Comput. Mater. Sci. 98 88 (2015)
  88. Semenov A S i dr. Fundamental’nye Problemy Sovremennogo Materialovedeniya 12 (1) 26 (2015)
  89. Dmitriev S V, Chetverikov A P, Velarde M G Phys. Stat. Solidi B 252 1682 (2015)
  90. Hizhnyakov V et al. Nucl. Instrum. Meth. Phys. Res. B 303 91 (2013)
  91. Kistanov A A i dr. Pis’ma ZhETF 99 403 (2014); Kistanov A A et al. JETP Lett. 99 353 (2014)
  92. Kistanov A A, Semenov A S, Dmitriev S V Zh. Eksp. Teor. Fiz. 146 869 (2014); Kistanov A A, Semenov A S, Dmitriev S V JETP 119 766 (2014)
  93. Kistanov A A et al. Eur. Phys. J. B 87 211 (2014)
  94. Doi Y Phys. Rev. E 68 066608 (2003)
  95. Kistanov A A et al. Pis’ma ZhTF 40 (15) 58 (2014); Kistanov A A et al. Tech. Phys. Lett. 40 657 (2014)
  96. Terentyev D A et al. Modelling Simul. Mater. Sci. Eng. 23 085007 (2015)
  97. Manley M E et al. Sci. Rep. 1 4 (2011)
  98. Manley M E et al. Phys. Rev. B 89 224106 (2014)
  99. Kempa M et al. Phys. Rev. B 89 054308 (2014)
  100. Eleftheriou M, Flach S, Tsironis G P Physica D 186 20 (2003)
  101. Ivanchenko M V et al. Physica D 198 120 (2004)
  102. Eleftheriou M, Flach S Physica D 202 142 (2005)
  103. Eleftheriou M, Flach S Low Temp. Phys. 34 554 (2008)
  104. Farago J Physica D 237 1013 (2008)
  105. Khadeeva L Z, Dmitriev S V Phys. Rev. B 84 144304 (2011)
  106. Xiong D et al. Phys. Rev. E 85 020102(R) (2012)
  107. Xiong D, Zhang Y, Zhao H Phys. Rev. E 88 052128 (2013)
  108. Xiong D, Zhang Y, Zhao H Phys. Rev. E 90 022117 (2014)
  109. Xiong D Europhys. Lett. 113 14002 (2016)
  110. Gaveau B et al. J. Luminescence 92 311 (2001)
  111. Mihokova E, Schulman L S J. Luminescence 129 1878 (2009)
  112. Yu G, Wang X, Tao Z Phys. Rev. E 83 026605 (2011)
  113. Markovich T et al. Phys. Rev. Lett. 88 195301 (2002)
  114. Zhang L, Tang G, Ma X Phys. Lett. A 374 2137 (2010)
  115. Russell F M, Eilbeck J C Europhys. Lett. 78 10004 (2007)
  116. Russell F M Nature 216 907 (1967)
  117. Russell F M Phys. Lett. B 25 298 (1967)
  118. Russell F M Phys. Lett. A 130 489 (1988)
  119. Wallis R F, Mills D L, Boardman A D Phys. Rev. B 52 R3828 (1995)
  120. Rakhmanova S, Mills D L Phys. Rev. B 54 9225 (1996)
  121. Lai R, Kiselev S A, Sievers A J Phys. Rev. B 54 9225 (1996)
  122. Kavitha L et al. J. Magn. Magn. Mater. 401 394 (2016)
  123. Pylypchuk R L, Zolotaryuk Y Low Temp. Phys. 41 (9) 733 (2015)
  124. Sato M et al. J. Appl. Phys. 91 8676 (2002)
  125. Liang W, Vanacore G M, Zewail A H Proc. Natl. Acad. Sci. USA 111 5491 (2014)
  126. Chechin G M, Dzhelauhova G S, Mehonoshina E A Phys. Rev. E 74 036608 (2006)
  127. Malomed B A Phys. Rev. B 49 5962 (1994)
  128. Savin A V, Manevitch L I Phys. Rev. B 67 144302 (2003)
  129. Flach S, Kladko K, Willis C R Phys. Rev. E 50 2293 (1994)
  130. Sandusky K W, Page J B Phys. Rev. B 50 866 (1994)
  131. Aubry S Physica D 103 201 (1997)
  132. Koukouloyannis V, Ichtiaroglou S Physica D 201 65 (2005)
  133. Flach S, Kladko K, MacKay R S Phys. Rev. Lett. 78 1207 (1997)
  134. Feng B-F, Kawahara T Wave Motion 45 68 (2007)
  135. Kastner M Phys. Rev. Lett. 92 104301 (2004)
  136. Kastner M Nonlinearity 17 1923 (2004)
  137. Kosevich Yu A Phys. Lett. A 173 257 (1993)
  138. Kosevich Yu A Phys. Rev. B 47 3138 (1993)
  139. Marín J L, Russell F M, Eilbeck J C Phys. Lett. A 248 225 (1998)
  140. Marín J L, Eilbeck J C, Russell F M Lecture Notes Phys. 542 293 (2000)
  141. Marín J L, Eilbeck J C, Russell F M Phys. Lett. A 281 21 (2001)
  142. Bajars J, Eilbeck J C, Leimkuhler B Physica D 301-302 8 (2015)
  143. Bajars J, Eilbeck J C, Leimkuhler B Quodons In Mica. Nonlinear Localized Travelling Excitations In Crystals (Springer Series in Materials Science) Vol. 221 (Eds J F R Archilla et al.) (Heidelberg: Springer, 2015) p. 35
  144. Kistanov A A, Dmitriev S V Pis’ma ZhTF 39 (13) 78 (2013); Kistanov A A, Dmitriev S V Tech. Phys. Lett. 39 618 (2013)
  145. Dmitriev S V, Kistanov A A, Dubinko V I Quodons In Mica. Nonlinear Localized Travelling Excitations In Crystals (Springer Series in Materials Science) Vol. 221 (Eds J F R Archilla et al.) (Heidelberg: Springer, 2015) p. 205
  146. Kiselev S A, Bickham S R, Sievers A J Phys. Rev. B 48 13508 (1993)
  147. Korznikova E A i dr. Pis’ma ZhETF 103 303 (2016); Korznikova E A et al. JETP Lett. 103 (4) (2016)
  148. Timoshenko S P, Goodier J N Theory Of Elasticity (New York: McGraw-Hill, 1970); Per. na russk. yaz., Timoshenko S P, Gud’er Dzh Teoriya Uprugosti (M.: Nauka, 1975)
  149. Hirth J P, Lothe J Theory Of Dislocations (New York: McGraw-Hill, 1968); Per. na russk. yaz., Khirt Dzh, Lote I Teoriya Dislokatsii (M.: Atomizdat, 1972)
  150. Brovman E G, Kagan Yu M Usp. Fiz. Nauk 112 369 (1974); Brovman E G, Kagan Yu M Sov. Phys. Usp. 17 125 (1974)
  151. Gufan A Yu i dr. Fiz. Tverd. Tela 54 770 (2012); Gufan A Yu et al. Phys. Solid State 54 820 (2012)
  152. Daw M S, Baskes M I Phys. Rev. B 29 6443 (1984)
  153. Cuevas J et al. Phys. Lett. A 315 364 (2003)
  154. Cuevas J et al. Physica D 216 115 (2006)
  155. Cuevas J et al. Discrete Contin. Dyn. Syst. S 4 1057 (2011)
  156. de Andrade P C, Cândido L, Teixeira Rabelo J N Phys. Lett. A 379 1833 (2015)
  157. Ting J J-L, Peyrard M Phys. Rev. E 53 1011 (1996)
  158. Forinash K, Peyrard M, Malomed B Phys. Rev. E 49 3400 (1994)
  159. Thota M, Harne R L, Wang K W J. Appl. Phys. 117 074505 (2015)
  160. Schroder U, Bonart D, Mayer A P Physica B 219-220 390 (1996)
  161. Kivshar Yu S, Zhang F, Takeno S Physica D 119 125 (1998)
  162. Franchini A, Bortolani V, Wallis R F Phys. Rev. B 53 5420 (1996)
  163. Franchini A, Bortolani V, Wallis R F Surf. Sci. 502-503 458 (2002)
  164. Franchini A, Bortolani V, Wallis R F J. Phys. Condens. Matter 12 1 (2000)
  165. Kivshar Yu S, Zhang F, Takeno S Physica D 113 248 (1998)
  166. Savin A V, Kivshar Yu S Phys. Rev. B 81 165418 (2010)
  167. Tamm I Phys. Z. Sowjetunion 1 733 (1932)
  168. Shockley W Phys. Rev. 56 317 (1939)
  169. Zhu T, Li J Prog. Mater. Sci. 55 710 (2010)
  170. Ogata S et al. Phys. Rev. B 70 104104 (2004)
  171. Baimova J A et al. Phys. Rev. B 86 035427 (2012)
  172. Wang S Phys. Lett. A 191 261 (1994)
  173. Dmitriev S V, Baimova Yu A Zh. Tekh. Fiz. 81 (11) 71 (2011); Dmitriev S V, Baimova Yu A Tech. Phys. 56 1612 (2011)
  174. Velarde M G J. Comput. Appl. Math. 233 1432 (2010)
  175. Brizhik L et al. Phys. Rev. B 85 245105 (2012)
  176. Chetverikov A P, Ebeling W, Velarde M G Physica D 240 1954 (2011)
  177. Velarde M G et al. Europhys. Lett. 106 27004 (2014)
  178. Chetverikov A P et al. Eur. Phys. J. B 87 153 (2014)
  179. Chetverikov A P, Ebeling W, Velarde M G Eur. Phys. J. B 85 291 (2012)
  180. Cisneros-Akea L A, Cruzeiro L, Velarde M G Physica D 306 82 (2015)
  181. Chetverikov A P et al. Quodons In Mica. Nonlinear Localized Travelling Excitations In Crystals (Springer Series in Materials Science) Vol. 221 (Eds J F R Archilla et al.) (Heidelberg: Springer, 2015) p. 267
  182. Brizhik L S et al. Quodons In Mica. Nonlinear Localized Travelling Excitations In Crystals (Springer Series in Materials Science) Vol. 221 (Eds J F R Archilla et al.) (Heidelberg: Springer, 2015) p. 291
  183. Chetverikov A P, Ebeling W, Velarde M G Quodons In Mica. Nonlinear Localized Travelling Excitations In Crystals (Springer Series in Materials Science) Vol. 221 (Eds J F R Archilla et al.) (Heidelberg: Springer, 2015) p. 321
  184. Muto V, Scott A C, Christiansen P L Phys. Lett. A 136 33 (1989)
  185. Marchesoni F, Lucheroni C Phys. Rev. E 44 5303 (1991)
  186. Chetverikov A P, Ebeling W, Velarde M G Eur. Phys. J. B 88 202 (2015)
  187. Manley M E Acta Mater. 58 2926 (2010)
  188. Rinaldi S, Turilli G Phys. Rev. B 31 3051 (1985)
  189. Burlakov V M, Kiselev S A, Rupasov V I Phys. Lett. A 147 130 (1990)
  190. Burlakov V M, Kiselev S A, Rupasov V I Pis’ma ZhETF 51 481 (1990); Burlakov V M, Kiselev S A, Rupasov V I JETP Lett. 51 544 (1990)
  191. Cretegny T et al. Physica D 121 109 (1998)
  192. Dauxois T et al. Chaos 15 015110 (2005)
  193. Kosevich Yu A, Corso G Physica D 170 1 (2002)
  194. Kosevich Yu A, Lepri S Phys. Rev. B 61 299 (2000)
  195. Ikeda K et al. Physica D 225 184 (2007)
  196. Kivshar Yu S, Peyrard M Phys. Rev. A 46 3198 (1992)
  197. Kavitha L et al. J. Biol. Phys. 39 15 (2013)
  198. Doi Y, Nakatani A J. Phys. Soc. Jpn. 81 124402 (2012)
  199. Geniet F, Leon J Phys. Rev. Lett. 89 134102 (2002)
  200. Kevrekidis P G et al. Phys. Rev. E 70 066627 (2004)
  201. Maniadis P, Kopidakis G, Aubry S Physica D 216 121 (2006)
  202. Medvedev N N i dr. Pis’ma ZhTF 37 (3) 7 (2011); Medvedev N N et al. Tech. Phys. Lett. 37 98 (2011)
  203. Rössler T, Page J B Phys. Rev. B 62 11460 (2000)
  204. Rössler T, Page J B Phys. Lett. A 204 418 (1995)
  205. Rössler T, Page J B Physica B 219-220 387 (1996)
  206. Flach S, Kladko K Physica D 127 61 (1999)
  207. Aubry S Physica D 216 1 (2006)
  208. Yoshimura K, Doi Y Wave Motion 45 83 (2007)
  209. Aubry S, Cretegny T Phys. D 119 34 (1998)
  210. Zueco D et al. Phys. Rev. E 71 036613 (2005)
  211. Sato M et al. Chaos 25 103122 (2015)
  212. Hizhnyakov V et al. Quodons In Mica. Nonlinear Localized Travelling Excitations In Crystals (Springer Series in Materials Science) Vol. 221 (Eds J F R Archilla et al.) (Heidelberg: Springer, 2015) p. 229
  213. Susanto H et al. Phys. Rev. Lett. 99 214103 (2007)
  214. Kosevich Yu A, Manevitch L I, Savin A V Phys. Rev. E 77 046603 (2008)
  215. Albiez M et al. Phys. Rev. Lett. 95 010402 (2005)
  216. Archilla J F R et al. Phys. Rev. E 91 022912 (2015)
  217. Kosevich Yu A Phys. Rev. Lett. 71 2058 (1993)
  218. Kosevich Yu A, Khomeriki R, Ruffo S Europhys. Lett. 66 21 (2004)
  219. Chechin G M, Lobzenko I P Pis’ma Materialakh 4 226 (2014)
  220. Lobzenko I P i dr. Fiz. Tverd. Tela 58 616 (2016); Lobzenko I P et al. Phys. Solid State 58 633 (2016)
  221. Lebedieva T et al. Nanoscale Res. Lett. 10 287 (2015)
  222. Bezuglova G S, Chechin G M, Goncharov P P Phys. Rev. E 84 036606 (2011)
  223. Chechin G M, Zhukov K G Phys. Rev. E 73 036216 (2006)
  224. Chechin G M, Ryabov D S, Shcherbinin S A Pis’ma Materialakh 6 9 (2016)
  225. Bishop A R et al. Phys. Rev. B 81 064106 (2010)
  226. Macutkevic J et al. Phys. Rev. B 83 184301 (2011)
  227. Glensk A et al. Phys. Rev. X 4 011018 (2014)
  228. Archilla J F R et al. J. Phys. Chem. B 110 24112 (2006)
  229. Dubinko V I, Selyshchev P A, Archilla J F R Phys. Rev. E 83 041124 (2011)
  230. Dubinko V I, Archilla J F R, Dmitriev S V, Hizhnyakov V Quodons In Mica. Nonlinear Localized Travelling Excitations In Crystals (Springer Series in Materials Science) Vol. 221 (Eds J F R Archilla et al.) (Heidelberg: Springer, 2015) p. 381
  231. Dubinko V I, Dubinko A V Nucl. Instrum. Meth. Phys. Res. B 303 133 (2013)
  232. Dubinko V I, Guglya A G, Donnelly S E Nucl. Instrum. Meth. Phys. Res. B 269 1634 (2011)
  233. Dubinko V I, Russell F M J. Nucl. Mater. 419 378 (2011)
  234. Dubinko V I i dr. Fiz. Tverd. Tela 54 2314 (2012); Dubinko V I et al. Phys. Solid State 54 2442 (2012)
  235. Dubinko V I, Dubinko A V, Dmitriev S V Pis’ma Materialakh 3 239 (2013)
  236. Karasev V S, Grinik E U Atomnaya Energiya 54 177 (1983); Grinik É U, Karasev V S Sov. Atom. Energy 54 184 (1983)
  237. Dubinko V, Shapovalov R Localized Excitations In Nonlinear Complex Systems. Current State Of The Art And Future Perspectives (Nonlinear Systems and Complexity) Vol. 7 (Eds R Carretero-González et al.) (Berlin: Springer, 2014) p. 265
  238. Dubinko V Pis’ma Materialakh 4 283 (2014)
  239. Dmitriev S V i dr. Izv. Vuzov. Fizika 51 (8) 73 (2008); Dmitriev S V et al. Russ. Phys. J. 51 858 (2008)
  240. Manevitch L I, Savin A V, Lamarque C-H Phys. Rev. B 74 014305 (2006)
  241. Manevitch L I, Savin A V, Lamarque C-H Physica D 237 600 (2008)

© 1918–2020 Uspekhi Fizicheskikh Nauk
Email: ufn@ufn.ru Editorial office contacts About the journal Terms and conditions