Integral criteria of wave collapses

Radiophysics and Quantum Electronics

Volumn 46, Issue 5-6, 2003, Pages 307-322

  Kuznetsov, E A ^a  

^a LANDAU INSTITUTE FOR THEORETICAL PHYSICS   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

ELECTRON OPTICS; MAGNETIC MATERIALS;

DIFFERENTIAL INEQUALITIES; DINGER EQUATION; GORDON EQUATION; LANDAU EQUATION; NONLINEAR STRINGS; SECOND ORDERS; TIME DEPENDENT; WAVE COLLAPSE;

NONLINEAR EQUATIONS;

EID: 84866559411     PISSN: 00338443     EISSN: 15739120     Source Type: Journal    
DOI: 10.1023/A:1026355431307     Document Type: Article

References (46)

1. S. N. Vlasov, V. A. Petrishchev, and V. I. Talanov, Radiophys. Quantum Electron., 14, No. 9, 1062 (1971).
2. V. E. Zakharov and E. A. Kuznetsov, Sov. Phys. JETP, 64, 773 (1986).
3. E. P. Gross, Nuovo Cimento, 20, 454 (1961).
4. L. P. Pitaevskii, Sov. Phys. JETP, 13, 451 (1961).
5. V. Flambaum and E. Kuznetsov, in: E. Caflisch and G. Papanicolaou, eds., Proc. NATO ARW ”Singu-larities in Fluids, Optics and Plasmas,” Kluwer (1993), p. 197.
6. L. Berge and J. J. Rasmussen, Phys. Lett. A, 304, 136 (2002).
7. V. I. Talanov, JETP Lett., 11, 199 (1970).
8. S. N. Vlasov and V. I. Talanov (1984), private comm.
9. E. A. Kuznetsov and S. K. Turitsyn, Phys. Lett. A, 112, 273 (1985).
10. S. N. Vlasov and V. I. Talanov, Self-Focusing of Waves [in Russian], Inst. Appl. Phys. Rus. Acad. Sci., Nizhny Novgorod (1997).
11. V. E. Zakharov, Sov. Phys. JETP, 35, 908 (1972).
12. H. A. Levine, Trans. Am. Math. Soc., 192, 1 (1974).
13. E. A. Kuznetsov, J. J. Rasmussen, K. Rypdal, and S. K. Turitsyn, Physica D, 87, 273 1995).
14. V. Kalantarov and O. Ladyzhenskaya, J. Sov. Math., 10, 53 (1978).
15. V. E. Zakharov, Sov. Phys. JETP, 38, 108 (1974).
16. G. E. Fal’kovich, M. D. Spector, and S. K. Turitsyn, Phys. Lett. A, 99, 271 (1983).
17. A. Yu. Orlov, “Soliton collapse in integrable systems,” Preprint Inst. Atomic Energy of the Siberian Branch of the Russian Acad. Sci., Novosibirsk (1983).
18. S. K. Turitsyn and G. E. Fal’kovich, Sov. Phys. JETP, 62, 146 (1985).
19. S. K. Turitsyn, Phys. Rev. E, 47, R13 (1993).
20. H. J. Fujita, Fac. Sci. Univ. Tokyo, Sect. A: Math., 16, 105 (1966).
21. S. K. Turitsyn, Phys. Rev. E, 47, R796 (1993).
22. E. A. Kuznetsov and P. M. Lushnikov, JETP, 81, 332 (1995).
23. L. Berge, E. A. Kuznetsov, and J. J. Rasmussen, Phys. Rev. E, 53, R1 340 (1996).
24. E. A. Kuznetsov, Physica D (2003), accepted (http://ru.arxiv.org/pdf/physics/0204080).
25. V. E. Zakharov and E. A. Kuznetsov, Sov. Phys. JETP, 39, 285 (1974).
26. E. A. Kuznetsov, A. M. Rubenchik, and V. E. Zakharov, Phys. Rep., 142, 103 (1986).
27. M. I. Weinstein, Commun. Math. Phys., 87, 567 (1983).
28. J. J. Rasmussen and K. Rypdal, Physica Scripta, 33, 481 (1986).
29. N. G. Vakhitov and A. A. Kolokolov, Radiophys. Quantum Electron., 16, 783 (1973).
30. L. Nirenberg, Ann. Sci. Norm. Sup. Pisa, 20, No. 4, 73 (1966).
31. O. A. Ladyzhenskaya, The Mathematical Theory of Viscous Incompressible Flow, Gordon and Breach, New York (1969).
32. P. A. Belanger, J. Opt. Soc. Am. B, 8, 2077 (1991).
33. W. Schopf and L. Kramer, Phys. Rev. Lett., 66, 2316 (1991).
34. E. Kaplan, E. Kuznetsov, and V. Steinberg, Phys. Rev. E, 50, 3712 (1994).
35. A. N. Kolmogorov, I. G. Petrovsky, and N. S. Piskunov, Bulletin Moscow State Univ. Math. Mech., 1, 1 (1937).
36. Ya. B. Zeldovich, Astron. Astrophys., 5, 84 (1970).
37. U. Frisch, Turbulence. The Legacy of A. N. Kolmogorov, Cambridge Univ. Press (1995).
38. V. E. Zakharov, S. V. Manakov, S. P. Novikov, and L. P. Pitaevsky, Soliton Theory. The Method of Inverse Problem, Plenum, New York (1984).
39. V. E. Zakharov, J. Appl. Mech. Tech. Phys., 9, 190 (1968).
40. A. G. Litvak, T. A. Petrova, A. M. Sergeev, and A. D. Yunakovskii, Sov. J. Plasma Phys., 9, 287 (1983).
41. N. A. Zharova, A. G. Litvak, T. A. Petrova, A. M. Sergeev, and A. D. Yunakovskii, JETP Lett., 44, 13 (1986).
42. E. A. Kuznetsov, S. L. Musher, and A. V. Shafarenko, JETP Lett., 37, 241 (1983).
43. E. A. Kuznetsov and S. L. Musher, JETP, 64, 947 (1986).
44. L. Bergé, K. Germaschewski, R. Grauer, and J. J. Rasmussen, Phys. Rev. Lett., 89, article No. 153902, (2002).
45. N. A. Zharova, A. G. Litvak, and V. A. Mironov, JETP Lett., 75, 539 (2002).
46. N. A. Zharova, A. G. Litvak, and V. A. Mironov, JETP, 96, No. 4, 643 (2003).