Abstract

The exact sufficient criterion of the collapse is found for the nonlinear spatiotemporal pulse dynamics in a periodic waveguide. A new method to prove the blowup of the initial pulse is described.

© 1993 Optical Society of America

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References

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  1. Y. Silberberg, Opt. Lett. 15, 1282 (1990).
    [Crossref] [PubMed]
  2. J. E. Rothenberg, Opt. Lett. 17, 584 (1992).
  3. A. B. Aceves, C. De Angelis, Opt. Lett. 18, 110 (1993).
    [Crossref] [PubMed]
  4. C. M. de Sterke, J. E. Sipe, Phys. Rev. A 38, 5149 (1988).
    [Crossref] [PubMed]
  5. D. N. Christodoulides, R. I. Joseph, Phys. Rev. Lett. 62, 1746 (1989).
    [Crossref] [PubMed]
  6. A. B. Aceves, S. Wabnitz, Phys. Lett. A141, 37 (1989).
  7. V. N. Vlasov, I. A. Petrischev, V. I. Talanov, Izv. Vys. Uchebn. Zaved. Radiofiz. 14, 1352 (1971).
  8. J. Rasmussen, K. Rypdal, Phys. Scr. 33, 481 (1986).
    [Crossref]
  9. V. E. Zakharov, V. S. Synakh, Sov. Phys. JETP 41, 465 (1976).
  10. S. K. Turitsyn, in Singularities in Fluids, Plasmas and Optics, R. Caflisch, ed. (Kluwer Academic, Dordrecht, The Netherlands, 1992), p. 63.
  11. S. K. Turitsyn, Phys. Rev. A 47, R27 (1993).
    [Crossref] [PubMed]

1993 (2)

1992 (1)

J. E. Rothenberg, Opt. Lett. 17, 584 (1992).

1990 (1)

1989 (2)

D. N. Christodoulides, R. I. Joseph, Phys. Rev. Lett. 62, 1746 (1989).
[Crossref] [PubMed]

A. B. Aceves, S. Wabnitz, Phys. Lett. A141, 37 (1989).

1988 (1)

C. M. de Sterke, J. E. Sipe, Phys. Rev. A 38, 5149 (1988).
[Crossref] [PubMed]

1986 (1)

J. Rasmussen, K. Rypdal, Phys. Scr. 33, 481 (1986).
[Crossref]

1976 (1)

V. E. Zakharov, V. S. Synakh, Sov. Phys. JETP 41, 465 (1976).

1971 (1)

V. N. Vlasov, I. A. Petrischev, V. I. Talanov, Izv. Vys. Uchebn. Zaved. Radiofiz. 14, 1352 (1971).

Aceves, A. B.

A. B. Aceves, C. De Angelis, Opt. Lett. 18, 110 (1993).
[Crossref] [PubMed]

A. B. Aceves, S. Wabnitz, Phys. Lett. A141, 37 (1989).

Christodoulides, D. N.

D. N. Christodoulides, R. I. Joseph, Phys. Rev. Lett. 62, 1746 (1989).
[Crossref] [PubMed]

De Angelis, C.

de Sterke, C. M.

C. M. de Sterke, J. E. Sipe, Phys. Rev. A 38, 5149 (1988).
[Crossref] [PubMed]

Joseph, R. I.

D. N. Christodoulides, R. I. Joseph, Phys. Rev. Lett. 62, 1746 (1989).
[Crossref] [PubMed]

Petrischev, I. A.

V. N. Vlasov, I. A. Petrischev, V. I. Talanov, Izv. Vys. Uchebn. Zaved. Radiofiz. 14, 1352 (1971).

Rasmussen, J.

J. Rasmussen, K. Rypdal, Phys. Scr. 33, 481 (1986).
[Crossref]

Rothenberg, J. E.

J. E. Rothenberg, Opt. Lett. 17, 584 (1992).

Rypdal, K.

J. Rasmussen, K. Rypdal, Phys. Scr. 33, 481 (1986).
[Crossref]

Silberberg, Y.

Sipe, J. E.

C. M. de Sterke, J. E. Sipe, Phys. Rev. A 38, 5149 (1988).
[Crossref] [PubMed]

Synakh, V. S.

V. E. Zakharov, V. S. Synakh, Sov. Phys. JETP 41, 465 (1976).

Talanov, V. I.

V. N. Vlasov, I. A. Petrischev, V. I. Talanov, Izv. Vys. Uchebn. Zaved. Radiofiz. 14, 1352 (1971).

Turitsyn, S. K.

S. K. Turitsyn, Phys. Rev. A 47, R27 (1993).
[Crossref] [PubMed]

S. K. Turitsyn, in Singularities in Fluids, Plasmas and Optics, R. Caflisch, ed. (Kluwer Academic, Dordrecht, The Netherlands, 1992), p. 63.

Vlasov, V. N.

V. N. Vlasov, I. A. Petrischev, V. I. Talanov, Izv. Vys. Uchebn. Zaved. Radiofiz. 14, 1352 (1971).

Wabnitz, S.

A. B. Aceves, S. Wabnitz, Phys. Lett. A141, 37 (1989).

Zakharov, V. E.

V. E. Zakharov, V. S. Synakh, Sov. Phys. JETP 41, 465 (1976).

Izv. Vys. Uchebn. Zaved. Radiofiz. (1)

V. N. Vlasov, I. A. Petrischev, V. I. Talanov, Izv. Vys. Uchebn. Zaved. Radiofiz. 14, 1352 (1971).

Opt. Lett. (3)

Phys. Lett. (1)

A. B. Aceves, S. Wabnitz, Phys. Lett. A141, 37 (1989).

Phys. Rev. A (2)

S. K. Turitsyn, Phys. Rev. A 47, R27 (1993).
[Crossref] [PubMed]

C. M. de Sterke, J. E. Sipe, Phys. Rev. A 38, 5149 (1988).
[Crossref] [PubMed]

Phys. Rev. Lett. (1)

D. N. Christodoulides, R. I. Joseph, Phys. Rev. Lett. 62, 1746 (1989).
[Crossref] [PubMed]

Phys. Scr. (1)

J. Rasmussen, K. Rypdal, Phys. Scr. 33, 481 (1986).
[Crossref]

Sov. Phys. JETP (1)

V. E. Zakharov, V. S. Synakh, Sov. Phys. JETP 41, 465 (1976).

Other (1)

S. K. Turitsyn, in Singularities in Fluids, Plasmas and Optics, R. Caflisch, ed. (Kluwer Academic, Dordrecht, The Netherlands, 1992), p. 63.

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Equations (10)

Equations on this page are rendered with MathJax. Learn more.

i U z + 2 U x 2 + σ 2 U t 2 + 2 | U | 2 U + cos ( q x ) U = 0.
i U z = δ H δ U * ,
H = + + [ | U x | 2 + σ | U t | 2 | U | 4 cos ( q x ) | U | 2 ] d x d t .
2 z 2 S = 8 H + 4 | U | 2 ( 2 cos q x q x sin q x ) d x d t .
S z z 8 ( H + N ) + 4 q S 1 / 2 N 1 / 2 = U ( S ) S ,
H + N 0 ,
½ S z 2 ½ S 0 z 2 + U ( S 0 ) U ( S ) = E U ( S ) .
S S 0 d s E U ( s ) 2 z .
H + N 0 ,
S | z = 0 < S m = ( 2 A / 3 B ) 2 ,

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