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Solitons and their interactions in classical field theory

,
Russian Federation State Scientific Center ‘A.I. Alikhanov Institute of Theoretical and Experimental Physics’, ul. Bolshaya Cheremushkinskaya 25, Moscow, 117259, Russian Federation

Effects of nonlinearity in the classical field theory for non-integrable systems are considered, such as soliton scattering, soliton bound states, the fractal nature of resonant structures, kink scattering by inhomogeneities, and bubble collapse. The results are presented in both (1 + 1) and higher dimensions. Both neutral and charged scalar fields are considered. Possible application areas for the nonlinearity effects are discussed.

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Fulltext is also available at DOI: 10.1070/PU1997v040n04ABEH000227
PACS: 03.50.−z, 03.50.Kk, 52.35.Py, 52.35.Sb (all)
DOI: 10.1070/PU1997v040n04ABEH000227
URL: https://ufn.ru/en/articles/1997/4/b/
A1997XB47600002
Citation: Belova T I, Kudryavtsev A E "Solitons and their interactions in classical field theory" Phys. Usp. 40 359–386 (1997)
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Îðèãèíàë: Áåëîâà Ò È, Êóäðÿâöåâ À Å «Ñîëèòîíû è èõ âçàèìîäåéñòâèÿ â êëàññè÷åñêîé òåîðèè ïîëÿ» ÓÔÍ 167 377–406 (1997); DOI: 10.3367/UFNr.0167.199704b.0377

References (179) ↓ Cited by (124) Similar articles (20)

  1. Higgs P W Phys. Rev. 145 1156 (1966)
  2. Weinberg S Phys. Rev. Lett. 19 1264 (1967); 31 494 (1973)
  3. Salam A "Elementary particle theory", in Proc. of the 8th Nobel Symposium (Stockholm, 1968)
  4. Okun’ L B Leptony i Kvarki (Leptons and Quarks, Moscow: Nauka, 1990) [Translated into English (Amsterdam, New York: North Holland, Elsevier, 1984)]
  5. Manton N S Commun. Math. Phys. 111 469 (1987)
  6. Rajaraman R Phys. Rep. Phys. Lett. C 21 227 (1975)
  7. Makhan’kov V G, Rybakov Yu P, Sanyuk V I Usp. Fiz. Nauk 164 121 (1994) [Phys. Usp. 37 113 (1994)]
  8. Kudryavtsev A, Piette B, Zakrzewski W J Z. Phys. C 60 731 (1993)
  9. Longren K, Scott E (Eds) Solitony v Deistvii (Solitons in Action, Moscow: Mir, 1981)
  10. Zakharov V E et al. Teoriya Solitonov: Metod Obratnoi Zadachi Rasseyaniya (Theory of Solitons: the Inverse Scattering Method, Moscow: Nauka, 1980) [Translated into English (New York: Consaltants Burean, 1984)]
  11. Ablowits M, Sigur H Solitony i Metod Obratnoi Zadachi (Solitons and Method of Inverse Scattering Problem, Moscow: Mir, 1987)
  12. Zakharov V E, Takhtadzhyan L A, Faddeev L D Dokl. Akad. Nauk SSSR 219 1334 (1974) [Sov. Phys. Dokl. 19 824 (1975)]
  13. Vergeles S N, Gryanik V M Yad. Fiz. 23 (6) 1324 (1976)
  14. Dodd R et al. Solitony i Nelineinye Volnovye Uravneniya (Solitons and Nonlinear Wave Equations, Moscow: Mir, 1988)
  15. Makhankov V G Phys. Rep. 35 1 (1978)
  16. Rajaraman R Solitony i Instantony v Kvantovoi Teorii Polya (Solitons and Instantons in Quantum Field Theory, Moscow: Mir, 1985)
  17. Hobart R H Proc. Phys. Soc. 82 201 (1963)
  18. Derrick G H J. Math. Phys. 5 1252 (1964)
  19. Zastavenko L G Fiz. Metody Metalloved. 29 430 (1965)
  20. Morawetz C S Proc. R. Soc. London Ser. A 306 291 (1968)
  21. Polyakov A M Pis’ma Zh. Eksp. Teor. Fiz. 20 430 (1974) [JETP Lett. 20 194 (1974)]
  22. Skyrme T H R Proc. R. Soc. London Ser. A 260 127 (1961)
  23. Piette B M A G, Shroers B J, Zakrzewski W J Nucl. Phys. B 439 205 (1995)
  24. Smilga A V Nucl. Phys. B 459 263 (1996)
  25. Zel’dovich Ya B, Kobzarev I Yu, Okun’ L B Zh. Eksp. Teor. Fiz. 67 3 (1974) [Sov. Phys. JETP 40 1 (1975)]
  26. Voloshin M B, Kobzarev I Yu, Okun’ L B Yad. Fiz. 20 1229 (1974)
  27. Kobzarev I Yu "Spontanno Narushennaya Simmetriya i Kosmologiya" (Spontaneously Violated Symmetry and Cosmology), in Œlementarnye Chastitsy. Vtoraya Shkola Fiziki ITEF (Elementary Particles. Second School of Physics at Institute for Theoretical and Experimental Physics) No. 3 (Moscow: Atomizdat, 1975); Coleman S Phys. Rev. D 15 2929 (1977); Callan C G, Coleman S Phys. Rev. D 16 1762 (1977)
  28. Anderson D L T, Derrick G H J. Math. Phys. 11 1336 (1970)
  29. Lee T D, Pang Y Phys. Rep. 221 251 (1992)
  30. Makhan’kov V G Fiz. Elem. Chastits At. Yadra 14 123 (1983) [Sov. J. Part. Nucl. 14 50 (1983)]
  31. Ginzburg V L, Landau L D Zh. Eksp. Teor. Fiz. 20 1064 (1950)
  32. Aubry S J. Chem. Phys. 64 3392 (1976)
  33. Krumhansl J A, Schrieffer J R Phys. Rev. B 11 3535 (1975)
  34. Rasizade O Sh Teor. Mat. Fiz. 48 197 (1981) [Theor. Math. Phys. 48 696 (1981)]
  35. Cahill K Phys. Lett. B 53 174 (1974)
  36. Shapiro I S Pis’ma Zh. Eksp. Teor. Fiz. 21 624 (1975) [JETP Lett. 21 293 (1975)]
  37. Dashen R F, Hasslacher B, Neveu A Phys. Rev. D 10 4130 (1974)
  38. Goldstone J, Jackiw R Phys. Rev. D 11 1486 (1975)
  39. Shapiro I S Zh. Eksp. Teor. Fiz. 70 2050 (1976) [Sov. Phys. JETP 43 1069 (1976)]
  40. Perring J K, Skyrme T H R Nucl. Phys. 31 550 (1962)
  41. Takhtadzhyan L A, Faddeev L D Teor. Mat. Fiz. 21 160 (1974)
  42. Gaudrey P J, Eilbeck J C, Gibbon J D Nuovo Cimento B 25 497 (1975)
  43. Dashen R F, Hasslacher B, Neveu A Phys. Rev. D 11 3424 (1975)
  44. Ablowitz M J, Kaup D J, Newell A C, Segur H Phys. Rev. Lett. 30 1262 (1973)
  45. Kosevich A M, Kovalev A S Zh. Eksp. Teor. Fiz. 67 1793 (1974) [Sov. Phys. JETP 40 891 (1975)]
  46. Bogolyubov N N, Mitropol’skii Yu A Asimptoticheskie Metody v Teorii Nelineinykh Kolebanii (Asymptotic Methods in Theory of Nonlinear Oscillations, Moscow: Fizmatgiz, 1963) [Translated into English (New York: G & Br Science Publ., 1961)]
  47. Voronov N A, Kobzarev I Yu Pis’ma Zh. Eksp. Teor. Fiz. 24 576 (1976) [JETP Lett. 24 576 (1976)]
  48. Bogolyubskii I L Pis’ma Zh. Eksp. Teor. Fiz. 24 579 (1976) [JETP Lett. 24 535 (1976)]
  49. Glasko V B et al. Zh. Eksp. Teor. Fiz. 35 452 (1958) [Sov. Phys. JETP 35 312 1959)]
  50. Ryder G Pacific J. Math. 22 477 (1967)
  51. Zhidkov E P, Shirikov V P Zh. Vych. Mat. Mat. Fiz. 4 804 (1964)
  52. Buslaev V S Teor. Mat. Fiz. 31 23 (1977) [Teor. Math. Phys. 31 293 (1977)]
  53. Eleonskii V M et al. Teor. Mat. Fiz. 60 395 (1984)
  54. Belova T I et al. Zh. Eksp. Teor. Fiz. 73 1611 (1977) [Sov. Phys. JETP 46 846 (1977)]
  55. Segur H, Kruskal M D Phys. Rev. Lett. 58 747 (1987)
  56. Aref’eva I Ya, Korepin V E Pis’ma Zh. Eksp. Teor. Fiz. 20 680 (1974) [JETP Lett. 20 312 (1974)]
  57. Korepin V E, Kilish P P, Faddeev L D Pis’ma Zh. Eksp. Teor. Fiz. 21 302 (1975) [JETP Lett. 21 138 (1975)]
  58. Faddeev L D Pis’ma Zh. Eksp. Teor. Fiz. 21 141 (1975) [JETP Lett. 21 64 (1975)]
  59. Dashen R F, Hasslacher B, Neveu A Phys. Rev. D 10 4114 (1974)
  60. Zamolodchnikov A B Pis’ma Zh. Eksp. Teor. Fiz. 25 499 (1977) [JETP Lett. 25 468 (1977)]
  61. Konoplich R V Yad. Fiz. 32 1132 (1980)
  62. Kudryavtsev A E Pis’ma Zh. Eksp. Teor. Fiz. 22 178 (1975) [JETP Lett. 22 82 (1975)]
  63. Neveu A, Papanicolaou N Commun. Math. Phys. 58 31 (1978)
  64. Belova T I et al. Preprint ITEF-170 (Moscow, 1976)
  65. Getmanov B S Pis’ma Zh. Eksp. Teor. Fiz. 24 323 (1976) [JETP Lett. 24 291 (1976)]
  66. Geicke J Phys. Lett. B 133 337 (1983)
  67. Belova T I Zh. Eksp. Teor. Fiz. 109 1090 (1996); Preprint ITEF-65 (Moscow, 1992) [JETP 82 587 (1996)]
  68. Segur H J Math. Phys. 24 1439 (1983)
  69. Konoplich R V Yad. Fiz. 24 1493 (1990)
  70. Gervais J-L, Sakita B Phys. Rev. D 11 2943 (1975)
  71. Gervais J-L, Jevicki A, Sakita B Phys. Rev. D 12 1038 (1975)
  72. Christ N H, Lee T D Phys. Rev. D 12 1606 (1975)
  73. Hosoya A, Kikkawa K Nucl. Phys. B 101 271 (1975)
  74. Vinciarelli P Phys. Lett B 61 80 (1976)
  75. Korepin V E Pis’ma Zh. Eksp. Teor. Fiz. 23 224 (1976) [JETP Lett. 23 201 (1976)]
  76. Rajaraman R Phys. Rev. D 15 2866 (1977)
  77. Moshir M Nucl. Phys. B 185 318 (1981)
  78. Sugiyama T Prog. Theor. Phys. 61 1550 (1979)
  79. Manakov S V Pis’ma Zh. Eksp. Teor. Fiz. 25 589 (1977) [JETP Lett. 25 553 (1977)]
  80. Getmanov B S Phys. Lett. B 66 39 (1977)
  81. Ablowitz M J, Kruskal M D, Ladik J F SIAM J. Appl. Math. 36 428 (1979)
  82. Wingate C A, Ph. D. Thesis (Univ. of Illinois, 1978); SIAM J. Appl. Math. 43 120 (1983)
  83. Klein R et al. Ferroelectrics 26 721 (1980)
  84. Campbell D K, Schonfeld J F, Wingate C A Physica D 9 1 (1983)
  85. Campbell D, Peyrard M Physica D 18 47 (1986)
  86. Belova T I, Kudryavtsev A E, Preprint ITEP-94 (Moscow, 1985); Physica D 32 18 (1988)
  87. Anninos P, Oliveira S, Matzner R A Phys. Rev. D 44 1147 (1991)
  88. Wolf A et al. Physica D 16 285 (1985)
  89. Benettin G et al. Mechanica 15 9 (1980)
  90. Shimada I, Nagashima T Prog. Theor. Phys. 61 1605 (1979)
  91. Belova T I Yad. Fiz. 58 130 (1995) [Phys. At. Nucl. 58 124 (1995)]
  92. Jedyadev S, Schrieffer J R Syn. Metals 9 451 (1984)
  93. Remoissenet M, Peyrard M Solid State Commun. 31 229 (1979)
  94. Remoissenet M, Peyrard M J Phys. C: Solid State Phys. 14 L481 (1981)
  95. Peyrard M, Remoissenet M Phys. Rev. B 26 2886 (1982)
  96. Peyrard M, Campbell D K Physica D 9 33 (1983)
  97. Campbell D, Peyrard M, Sodano P Physica D 19 165 (1986)
  98. Maki K, Kumar P Phys. Rev. B 14 118 (1976); 3920
  99. Maki K Physica B 90 84 (1977)
  100. Kitchenside P W, Bullough R K, Caudrey P J, in Solitons in Condensed Matter Physics (Eds A R Bishop, T Schneider) p. 291 (Berlin: Springer, 1978)
  101. Bullough R K, Caudrey P J, Gibbs H M, in Solitons (Eds R K Bullough, P J Caudrey, Berlin: Springer, 1980) p. 107
  102. Shiefman J, Kumar P Physica Scripta 20 435 (1979)
  103. Kumar P, Holland R R, in Nonlinear Problems: Present and Future (Eds A R Bishop, D K Campbell, B Nikolaemko, Amsterdam: North-Holland, 1982) p. 229
  104. Condat C A, Guyer R A, Miller M D Phys. Rev. B 27 474 (1983)
  105. Fogel M B et al. Phys. Rev. B15 1578 (1977)
  106. Nakajima K, Yamashita T, Onodera Y J. Appl. Phys. 45 3141 (1974)
  107. Nakajima K et al. J. Appl. Phys. 45 4095 (1974)
  108. Nakajima K, Sawada Y, Onodera Y J. Appl. Phys. 46 5272 (1975)
  109. Karpman V I, Maslov E M Zh. Eksp. Teor. Fiz. 73 537 (1977) [Sov. Phys. JETP 46 281 (1977)]
  110. Bergman D J et al. Phys. Rev. A 27 3345 (1983)
  111. Olsen O H, Samuelsen M R Phys. Rev. B 28 210 (1983)
  112. Malomed B A Physics D 15 385 (1985)
  113. Jackiw R, Rossi P Phys. Rev. D 21 426 (1980)
  114. Rasizade O Sh Teor. Mat. Fiz. 49 36 (1981)
  115. Gal’pern Yu S, Filippov A T Pis’ma Zh. Eksp. Teor. Fiz. 35 470 (1982) [JETP Lett. 35 580 (1982)]
  116. Filippov A T, Galpern Yu S Solid State Commun. 48 665 (1983)
  117. Galpern Yu S, Filippov A T Zh. Eksp. Teor. Fiz. 86 1527 (1984) [Sov. Phys. JETP 59 894 (1984)]
  118. Currie J F et al. Phys. Rev. B15 5567 (1977)
  119. Kazacha G S, Serdyukova S I, Filippov A T, Preprint OIYaI R-11-84-76 (Dubna, 1984)
  120. Kazacha G S, Serdyukova S I, Filippov A T, Preprint OIYaI R-11-85-60 (Dubna, 1985)
  121. Filippov A T, Galpern Yu S Phys. Lett. A 172 471 (1993)
  122. Belova T I, Kudryavtsev A E, Preprint ITEP-170 (Moscow, 1986)
  123. Belova T I, Kudryavtsev A E Zh. Eksp. Teor. Fiz. 108 1489 (1995) [JETP 81 817 (1995)]; Kudryavtsev A E, Preprint INS-Rep. 912, Jan. (Tokyo, 1992)
  124. Toda M J. Phys. Soc. Japan 23 501 (1967)
  125. Toda M Prog. Theor. Phys. Suppl. 59 1 (1976)
  126. Nakamura A, Takeno S Prog. Theor. Phys. 58 1074 (1977)
  127. Fraggis T, Pnevmatikos St, Economou E N Phys. Lett. A 142 361 (1989)
  128. Kosevich A M, Kovalev A S Fiz. Nizk. Temp. 1 1544 (1975)
  129. Braun O M, Kivshar Yu Phys. Rev. B 43 1060 (1991)
  130. Fei Z et al. Phys. Lett. A 159 318 (1991)
  131. Kivshar Yu, Vazquez L Phys. Rev. Lett. 67 1177 (1991)
  132. Fei Z, Kivshar Yu, Vazquez L Phys. Rev A 45 6019 (1992)
  133. Fei Z, Kivshar Yu, Vazquez L Phys. Rev. A 46 5214 (1992)
  134. Grib A A, Damaskinskii E V, Maksimov V M Usp. Fiz. Nauk 102 587 (1970) [Sov. Phys. Usp. 13 798 (1971)]
  135. Voronov N A, Kobzarev I Yu, Konyukhova N B Pis’ma Zh. Eksp. Teor. Fiz. 22 590 (1975) [JETP Lett. 22 290 (1975)]
  136. Bogolyubskii I L, Makhan’kov V G Pis’ma Zh. Eksp. Teor. Fiz. 24 15 (1976) [JETP Lett. 24 12 (1976)]
  137. Christiansen P L, Olsen O H Physica Scripta 20 531 (1979)
  138. Belova T I Yad. Fiz. 56 (2) 234 (1993)
  139. Bogolyubskii I L, Makhan’kov V G Pis’ma Zh. Eksp. Teor. Fiz. 25 120 (1977) [JETP Lett. 25 107 (1977)]
  140. Bogolubsky I L Phys. Lett. A 61 205 (1977)
  141. Christiansen P L, Olsen O H Phys. Lett. A 68 185 (1978)
  142. Samuelsen M R Phys. Lett. A 74 21 (1979)
  143. Christiansen P L, Lomdahl P S Physica D 2 482 (1981)
  144. Geicke J Phys. Lett. A 98 147 (1983)
  145. Geicke J Physica Scripta 29 431 (1984)
  146. Voronov N A, Preprint ITEP-127 (Moscow, 1978)
  147. Voronov N A, Konyukhova N B, Preprint ITEP-26 (Moscow, 1978)
  148. Kivshar Yu, Malomed B A Phys. Rev. Lett. 60 164 (1988)
  149. Malomed B A Physica D 24 155 (1987)
  150. Malomed B A, Maslov E M Phys. Lett A 160 233 (1991)
  151. Belova T I et al. Zh. Vych. Mat. Mat. Fiz. 21 89 (1981)
  152. Anderson D L T J. Math. Phys. 12 945 (1971)
  153. Friedberg R, Lee T D, Sirlin A Phys. Rev. D 13 2739 (1976)
  154. Friedberg R, Lee T D, Sirlin A Nucl. Phys. B 115 1 (1976)
  155. Friedberg R, Lee T D, Sirlin A Nucl. Phys. B 115 32 (1976)
  156. Coleman S Nucl. Phys. B 262 263 (1985)
  157. Wilets N Non-topological Solitons, Lecture Notes in Physics 24 (Singapore: World Scientific, 1989)
  158. Birse M Soliton Models for Nuclear Physics Manchester Univ. Preprint (Manchester, 1980)
  159. Tomboulis E Phys. Rev. D 12 1678 (1975)
  160. Belova T I et al. Yad. Fiz. 57 2105 (1994) [Phys. At. Nucl. 57 2028 (1994)]; Preprint ITEF-166 (Moscow, 1982)
  161. Zakharov V E, Shabad A B Zh. Eksp. Teor. Fiz. 61 118 (1971) [Sov. Phys. JETP (1971)]
  162. Belova T I, Kudryavtsev A E Zh. Eksp. Teor. Fiz. 95 13 (1989) [Sov. Phys. JETP 68 7 (1989)]
  163. Simonov Yu A Yad. Fiz. 30 1148 (1979)
  164. Simonov Yu A Yad. Fiz. 30 1457 (1979)
  165. Leese R A Nucl. Phys. B 366 283 (1991)
  166. Getmanov B S, Preprint OIYaI P2-10208 (Dubna, 1976)
  167. Belova T I, Voronov N A Pis’ma Zh. Eksp. Teor. Fiz. 61 337 (1995) [JETP Lett. 61 341 (1995)]
  168. Hawking S W, Moss I G, Stewart J M Phys. Rev. D 26 2681 (1982)
  169. Widrow L M Phys. Rev. D 40 1002 (1989)
  170. Kolb E W, Turner M S The Early Universe (Redwood City, Ca: Addison-Wiley, 1990)
  171. Linde A Phys. Rev. D 49 748 (1994)
  172. Vilenkin A Phys. Rep. 121 263 (1985)
  173. Colpi M, Shapiro S L, Wasserman I Phys. Rev. Lett. 57 2485 (1986)
  174. Jetzer P Phys. Rep. 220 163 (1992)
  175. Pushkarov D I Defektony v Kristallakh. Metod Kvazichastits v Kvantovoi Teorii Defektov (Defectons in Crystals. Method of Quasi-particles in Quantum Theory of Defects, Moscow: Nauka, 1993)
  176. Monastyrskii M I Topologiya Kalibrovochnykh Polei i Kondensirovannykh Sred (Topology of Calibration Fields and Condensed Media, Moscow: PAIMS, 1995) [in English (New York: Plenum Press, 1993)]
  177. Zosimov V V, Lyamshev L N Usp. Fiz. Nauk 165 361 (1995) [Phys. Usp. 38 347 (1995)]
  178. Loshak P Usp. Mat. Nauk 47 59 (1992)
  179. Kadomtsev B B Usp. Fiz. Nauk 164 449 (1994) [Phys. Usp. 37 425 (1994)]

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