Abstract

We develop a theory of soliton interactions in a bulk χ(2) medium. In particular, we derive a general analytical model based on the effective particle approach to predict the result of the soliton interactions and also verify the validity of the model by direct numerical simulations. Among the major phenomena investigated are soliton scattering, spiraling, and fusion and also power exchange between the colliding solitons.

© 1999 Optical Society of America

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  1. M. Segev and G. I. Stegeman, Phys. Today 51, 42 (1998), and references therein.
  2. K. A. Gorshkov and L. A. Ostrovsky, Physica D 3, 428 (1981).
  3. V. I. Karpman and V. V. Solov’ev, Physica D 3, 487 (1981).
  4. V. V. Steblina, Yu. S. Kivshar, and A. V. Buryak, Opt. Lett. 23, 156 (1998).
  5. W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. Van Stryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, Phys. Rev. Lett. 74, 5036 (1995).
  6. G. C. Duree, J. L. Shultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. Di Porto, E. J. Sharp, and R. R. Neurgaonkar, Phys. Rev. Lett. 71, 553 (1993).
  7. V. Tikhonenko, J. Christou, and B. Luther-Davies, J. Opt. Soc. Am. B 12, 2046 (1995).
  8. V. Tikhonenko, J. Christou, and B. Luther-Davies, Phys. Rev. Lett. 76, 2698 (1996).
  9. M. Shih, M. Segev, and G. Salamo, Phys. Rev. Lett. 78, 2551 (1997); A. V. Buryak, Yu. S. Kivshar, M. Shih, and M. Segev, Phys. Rev. Lett. (to be published).
  10. L. Poladian, A. W. Snyder, and D. J. Mitchell, Opt. Commun. 85, 59 (1991).
  11. A. V. Buryak, Yu. S. Kivshar, and V. V. Steblina, Phys. Rev. A 52, 1670 (1995).
  12. A. V. Buryak, Yu. S. Kivshar, and S. Trillo, Phys. Rev. Lett. 77, 5210 (1996).
  13. A. V. Buryak and Yu. S. Kivshar, Phys. Rev. Lett. 78, 3286 (1997).
  14. M. T. G. Canva, R. A. Fuerst, D. Baboiu, G. I. Stegeman, and G. Assanto, Opt. Lett. 22, 1683 (1997).
  15. R. A. Fuerst, M. T. G. Canva, D. Baboiu, and G. I. Stegeman, Opt. Lett. 22, 1748 (1997).
  16. G. I. Stegeman, D. J. Hagan, and L. Torner, Opt. Quantum Electron. 28, 1691 (1996).
  17. M. J. Werner and P. D. Drummond, J. Opt. Soc. Am. B 10, 2390 (1993).
  18. D. M. Baboiu, G. I. Stegeman, and L. Torner, Opt. Lett. 20, 2282 (1995).
  19. C. Etrich, U. Peschel, F. Lederer, and B. Malomed, Phys. Rev. A 52, R3444 (1995).
  20. M. Haelterman, S. Trillo, and P. Ferro, Opt. Lett. 22, 84 (1997).
  21. D. M. Baboiu and G. I. Stegeman, J. Opt. Soc. Am. B 14, 3143 (1997).
  22. G. Leo, G. Assanto, and W. E. Torruellas, Opt. Lett. 22, 7 (1997).
  23. G. Leo, G. Assanto, and W. E. Torruellas, Opt. Commun. 134, 223 (1997).
  24. C. Etrich, U. Peschel, F. Lederer, B. Malomed, and Yu. S. Kivshar, Phys. Rev. E 54, 4321 (1996); D. E. Pelenovsky, Yu. S. Kivshar, and V. V. Afanasjev, Physica D 116, 121 (1998); Yu. S. Kivshar, D. E. Pelenovsky, T. Cretegny, and M. Peyrard, Phys. Rev. Lett. PRLTAO 80, 5032 (1998).
  25. Y. Baek, R. Schiek, G. I. Stegeman, I. Baumann, and W. Sohler, Opt. Lett. 22, 1550 (1997).
  26. B. Costantini, C. De Angelis, A. Barthelemy, B. Bourliaguest, and V. Kermene, Opt. Lett. 23, 424 (1998).
  27. C. R. Menyuk, R. Schiek, and L. Torner, J. Opt. Soc. Am. B 11, 2434 (1994).
  28. A. V. Buryak and Yu. S. Kivshar, Phys. Lett. A 197, 407 (1995).
  29. A. V. Buryak, “Solitons due to second harmonic generation,” Ph.D. dissertation (Australian National University, Canberra, 1996).
  30. V. V. Steblina, Yu. S. Kivshar, M. Lisak, and B. A. Malomed, Opt. Commun. 118, 345 (1995).
  31. D. E. Pelinovsky, A. V. Buryak, and Yu. S. Kivshar, Phys. Rev. Lett. 75, 591 (1995).
  32. T. P. Taha and M. J. Ablowitz, J. Comput. Phys. 55, 203 (1984).
  33. H. Goldstein, Classical Mechanics (Addison-Wesley, Reading, Mass., 1980), Chap. 3.
  34. A. W. Snyder, A. V. Buryak, and D. J. Mitchell, Opt. Lett. 23, 4 (1998).
  35. A. V. Buryak, Yu. S. Kivshar, and S. Trillo, J. Opt. Soc. Am. B 14, 3110 (1997).
  36. G. D. Miller, R. G. Batchko, W. M. Tulloch, D. R. Weise, M. M. Fejer, and R. L. Byer, Opt. Lett. 22, 1834 (1997).
  37. D. E. Edmundson and R. H. Enns, Opt. Lett. 18, 1609 (1993).
  38. D. E. Edmundson and R. H. Enns, Phys. Rev. A 51, 2491 (1995).
  39. B. Malomed, P. Drummond, H. He, A. Berntson, D. Anderson, and M. Lisak, Phys. Rev. E 56, 4725 (1997).

1998 (4)

1997 (11)

1996 (3)

G. I. Stegeman, D. J. Hagan, and L. Torner, Opt. Quantum Electron. 28, 1691 (1996).

A. V. Buryak, Yu. S. Kivshar, and S. Trillo, Phys. Rev. Lett. 77, 5210 (1996).

V. Tikhonenko, J. Christou, and B. Luther-Davies, Phys. Rev. Lett. 76, 2698 (1996).

1995 (9)

A. V. Buryak, Yu. S. Kivshar, and V. V. Steblina, Phys. Rev. A 52, 1670 (1995).

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. Van Stryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, Phys. Rev. Lett. 74, 5036 (1995).

C. Etrich, U. Peschel, F. Lederer, and B. Malomed, Phys. Rev. A 52, R3444 (1995).

A. V. Buryak and Yu. S. Kivshar, Phys. Lett. A 197, 407 (1995).

V. V. Steblina, Yu. S. Kivshar, M. Lisak, and B. A. Malomed, Opt. Commun. 118, 345 (1995).

D. E. Pelinovsky, A. V. Buryak, and Yu. S. Kivshar, Phys. Rev. Lett. 75, 591 (1995).

V. Tikhonenko, J. Christou, and B. Luther-Davies, J. Opt. Soc. Am. B 12, 2046 (1995).

D. M. Baboiu, G. I. Stegeman, and L. Torner, Opt. Lett. 20, 2282 (1995).

D. E. Edmundson and R. H. Enns, Phys. Rev. A 51, 2491 (1995).

1994 (1)

1993 (3)

D. E. Edmundson and R. H. Enns, Opt. Lett. 18, 1609 (1993).

G. C. Duree, J. L. Shultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. Di Porto, E. J. Sharp, and R. R. Neurgaonkar, Phys. Rev. Lett. 71, 553 (1993).

M. J. Werner and P. D. Drummond, J. Opt. Soc. Am. B 10, 2390 (1993).

1991 (1)

L. Poladian, A. W. Snyder, and D. J. Mitchell, Opt. Commun. 85, 59 (1991).

1984 (1)

T. P. Taha and M. J. Ablowitz, J. Comput. Phys. 55, 203 (1984).

1981 (2)

K. A. Gorshkov and L. A. Ostrovsky, Physica D 3, 428 (1981).

V. I. Karpman and V. V. Solov’ev, Physica D 3, 487 (1981).

Ablowitz, M. J.

T. P. Taha and M. J. Ablowitz, J. Comput. Phys. 55, 203 (1984).

Anderson, D.

B. Malomed, P. Drummond, H. He, A. Berntson, D. Anderson, and M. Lisak, Phys. Rev. E 56, 4725 (1997).

Assanto, G.

Baboiu, D.

Baboiu, D. M.

Baek, Y.

Barthelemy, A.

Batchko, R. G.

Baumann, I.

Berntson, A.

B. Malomed, P. Drummond, H. He, A. Berntson, D. Anderson, and M. Lisak, Phys. Rev. E 56, 4725 (1997).

Bourliaguest, B.

Buryak, A. V.

A. W. Snyder, A. V. Buryak, and D. J. Mitchell, Opt. Lett. 23, 4 (1998).

V. V. Steblina, Yu. S. Kivshar, and A. V. Buryak, Opt. Lett. 23, 156 (1998).

A. V. Buryak, Yu. S. Kivshar, and S. Trillo, J. Opt. Soc. Am. B 14, 3110 (1997).

A. V. Buryak and Yu. S. Kivshar, Phys. Rev. Lett. 78, 3286 (1997).

A. V. Buryak, Yu. S. Kivshar, and S. Trillo, Phys. Rev. Lett. 77, 5210 (1996).

D. E. Pelinovsky, A. V. Buryak, and Yu. S. Kivshar, Phys. Rev. Lett. 75, 591 (1995).

A. V. Buryak, Yu. S. Kivshar, and V. V. Steblina, Phys. Rev. A 52, 1670 (1995).

A. V. Buryak and Yu. S. Kivshar, Phys. Lett. A 197, 407 (1995).

Byer, R. L.

Canva, M. T. G.

Christou, J.

V. Tikhonenko, J. Christou, and B. Luther-Davies, Phys. Rev. Lett. 76, 2698 (1996).

V. Tikhonenko, J. Christou, and B. Luther-Davies, J. Opt. Soc. Am. B 12, 2046 (1995).

Costantini, B.

Crosignani, B.

G. C. Duree, J. L. Shultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. Di Porto, E. J. Sharp, and R. R. Neurgaonkar, Phys. Rev. Lett. 71, 553 (1993).

De Angelis, C.

Di Porto, P.

G. C. Duree, J. L. Shultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. Di Porto, E. J. Sharp, and R. R. Neurgaonkar, Phys. Rev. Lett. 71, 553 (1993).

Drummond, P.

B. Malomed, P. Drummond, H. He, A. Berntson, D. Anderson, and M. Lisak, Phys. Rev. E 56, 4725 (1997).

Drummond, P. D.

Duree, G. C.

G. C. Duree, J. L. Shultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. Di Porto, E. J. Sharp, and R. R. Neurgaonkar, Phys. Rev. Lett. 71, 553 (1993).

Edmundson, D. E.

D. E. Edmundson and R. H. Enns, Phys. Rev. A 51, 2491 (1995).

D. E. Edmundson and R. H. Enns, Opt. Lett. 18, 1609 (1993).

Enns, R. H.

D. E. Edmundson and R. H. Enns, Phys. Rev. A 51, 2491 (1995).

D. E. Edmundson and R. H. Enns, Opt. Lett. 18, 1609 (1993).

Etrich, C.

C. Etrich, U. Peschel, F. Lederer, and B. Malomed, Phys. Rev. A 52, R3444 (1995).

Fejer, M. M.

Ferro, P.

Fuerst, R. A.

Gorshkov, K. A.

K. A. Gorshkov and L. A. Ostrovsky, Physica D 3, 428 (1981).

Haelterman, M.

Hagan, D. J.

G. I. Stegeman, D. J. Hagan, and L. Torner, Opt. Quantum Electron. 28, 1691 (1996).

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. Van Stryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, Phys. Rev. Lett. 74, 5036 (1995).

He, H.

B. Malomed, P. Drummond, H. He, A. Berntson, D. Anderson, and M. Lisak, Phys. Rev. E 56, 4725 (1997).

Karpman, V. I.

V. I. Karpman and V. V. Solov’ev, Physica D 3, 487 (1981).

Kermene, V.

Kivshar, Yu. S.

V. V. Steblina, Yu. S. Kivshar, and A. V. Buryak, Opt. Lett. 23, 156 (1998).

A. V. Buryak, Yu. S. Kivshar, and S. Trillo, J. Opt. Soc. Am. B 14, 3110 (1997).

A. V. Buryak and Yu. S. Kivshar, Phys. Rev. Lett. 78, 3286 (1997).

A. V. Buryak, Yu. S. Kivshar, and S. Trillo, Phys. Rev. Lett. 77, 5210 (1996).

D. E. Pelinovsky, A. V. Buryak, and Yu. S. Kivshar, Phys. Rev. Lett. 75, 591 (1995).

A. V. Buryak, Yu. S. Kivshar, and V. V. Steblina, Phys. Rev. A 52, 1670 (1995).

V. V. Steblina, Yu. S. Kivshar, M. Lisak, and B. A. Malomed, Opt. Commun. 118, 345 (1995).

A. V. Buryak and Yu. S. Kivshar, Phys. Lett. A 197, 407 (1995).

Lederer, F.

C. Etrich, U. Peschel, F. Lederer, and B. Malomed, Phys. Rev. A 52, R3444 (1995).

Leo, G.

G. Leo, G. Assanto, and W. E. Torruellas, Opt. Commun. 134, 223 (1997).

G. Leo, G. Assanto, and W. E. Torruellas, Opt. Lett. 22, 7 (1997).

Lisak, M.

B. Malomed, P. Drummond, H. He, A. Berntson, D. Anderson, and M. Lisak, Phys. Rev. E 56, 4725 (1997).

V. V. Steblina, Yu. S. Kivshar, M. Lisak, and B. A. Malomed, Opt. Commun. 118, 345 (1995).

Luther-Davies, B.

V. Tikhonenko, J. Christou, and B. Luther-Davies, Phys. Rev. Lett. 76, 2698 (1996).

V. Tikhonenko, J. Christou, and B. Luther-Davies, J. Opt. Soc. Am. B 12, 2046 (1995).

Malomed, B.

B. Malomed, P. Drummond, H. He, A. Berntson, D. Anderson, and M. Lisak, Phys. Rev. E 56, 4725 (1997).

C. Etrich, U. Peschel, F. Lederer, and B. Malomed, Phys. Rev. A 52, R3444 (1995).

Malomed, B. A.

V. V. Steblina, Yu. S. Kivshar, M. Lisak, and B. A. Malomed, Opt. Commun. 118, 345 (1995).

Menyuk, C. R.

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. Van Stryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, Phys. Rev. Lett. 74, 5036 (1995).

C. R. Menyuk, R. Schiek, and L. Torner, J. Opt. Soc. Am. B 11, 2434 (1994).

Miller, G. D.

Mitchell, D. J.

A. W. Snyder, A. V. Buryak, and D. J. Mitchell, Opt. Lett. 23, 4 (1998).

L. Poladian, A. W. Snyder, and D. J. Mitchell, Opt. Commun. 85, 59 (1991).

Neurgaonkar, R. R.

G. C. Duree, J. L. Shultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. Di Porto, E. J. Sharp, and R. R. Neurgaonkar, Phys. Rev. Lett. 71, 553 (1993).

Ostrovsky, L. A.

K. A. Gorshkov and L. A. Ostrovsky, Physica D 3, 428 (1981).

Pelinovsky, D. E.

D. E. Pelinovsky, A. V. Buryak, and Yu. S. Kivshar, Phys. Rev. Lett. 75, 591 (1995).

Peschel, U.

C. Etrich, U. Peschel, F. Lederer, and B. Malomed, Phys. Rev. A 52, R3444 (1995).

Poladian, L.

L. Poladian, A. W. Snyder, and D. J. Mitchell, Opt. Commun. 85, 59 (1991).

Salamo, G. J.

G. C. Duree, J. L. Shultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. Di Porto, E. J. Sharp, and R. R. Neurgaonkar, Phys. Rev. Lett. 71, 553 (1993).

Schiek, R.

Segev, M.

M. Segev and G. I. Stegeman, Phys. Today 51, 42 (1998), and references therein.

G. C. Duree, J. L. Shultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. Di Porto, E. J. Sharp, and R. R. Neurgaonkar, Phys. Rev. Lett. 71, 553 (1993).

Sharp, E. J.

G. C. Duree, J. L. Shultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. Di Porto, E. J. Sharp, and R. R. Neurgaonkar, Phys. Rev. Lett. 71, 553 (1993).

Shultz, J. L.

G. C. Duree, J. L. Shultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. Di Porto, E. J. Sharp, and R. R. Neurgaonkar, Phys. Rev. Lett. 71, 553 (1993).

Snyder, A. W.

A. W. Snyder, A. V. Buryak, and D. J. Mitchell, Opt. Lett. 23, 4 (1998).

L. Poladian, A. W. Snyder, and D. J. Mitchell, Opt. Commun. 85, 59 (1991).

Sohler, W.

Solov’ev, V. V.

V. I. Karpman and V. V. Solov’ev, Physica D 3, 487 (1981).

Steblina, V. V.

V. V. Steblina, Yu. S. Kivshar, and A. V. Buryak, Opt. Lett. 23, 156 (1998).

A. V. Buryak, Yu. S. Kivshar, and V. V. Steblina, Phys. Rev. A 52, 1670 (1995).

V. V. Steblina, Yu. S. Kivshar, M. Lisak, and B. A. Malomed, Opt. Commun. 118, 345 (1995).

Stegeman, G. I.

M. Segev and G. I. Stegeman, Phys. Today 51, 42 (1998), and references therein.

M. T. G. Canva, R. A. Fuerst, D. Baboiu, G. I. Stegeman, and G. Assanto, Opt. Lett. 22, 1683 (1997).

Y. Baek, R. Schiek, G. I. Stegeman, I. Baumann, and W. Sohler, Opt. Lett. 22, 1550 (1997).

D. M. Baboiu and G. I. Stegeman, J. Opt. Soc. Am. B 14, 3143 (1997).

R. A. Fuerst, M. T. G. Canva, D. Baboiu, and G. I. Stegeman, Opt. Lett. 22, 1748 (1997).

G. I. Stegeman, D. J. Hagan, and L. Torner, Opt. Quantum Electron. 28, 1691 (1996).

D. M. Baboiu, G. I. Stegeman, and L. Torner, Opt. Lett. 20, 2282 (1995).

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. Van Stryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, Phys. Rev. Lett. 74, 5036 (1995).

Taha, T. P.

T. P. Taha and M. J. Ablowitz, J. Comput. Phys. 55, 203 (1984).

Tikhonenko, V.

V. Tikhonenko, J. Christou, and B. Luther-Davies, Phys. Rev. Lett. 76, 2698 (1996).

V. Tikhonenko, J. Christou, and B. Luther-Davies, J. Opt. Soc. Am. B 12, 2046 (1995).

Torner, L.

G. I. Stegeman, D. J. Hagan, and L. Torner, Opt. Quantum Electron. 28, 1691 (1996).

D. M. Baboiu, G. I. Stegeman, and L. Torner, Opt. Lett. 20, 2282 (1995).

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. Van Stryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, Phys. Rev. Lett. 74, 5036 (1995).

C. R. Menyuk, R. Schiek, and L. Torner, J. Opt. Soc. Am. B 11, 2434 (1994).

Torruellas, W. E.

G. Leo, G. Assanto, and W. E. Torruellas, Opt. Commun. 134, 223 (1997).

G. Leo, G. Assanto, and W. E. Torruellas, Opt. Lett. 22, 7 (1997).

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. Van Stryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, Phys. Rev. Lett. 74, 5036 (1995).

Trillo, S.

Tulloch, W. M.

Van Stryland, E. W.

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. Van Stryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, Phys. Rev. Lett. 74, 5036 (1995).

Wang, Z.

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. Van Stryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, Phys. Rev. Lett. 74, 5036 (1995).

Weise, D. R.

Werner, M. J.

Yariv, A.

G. C. Duree, J. L. Shultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. Di Porto, E. J. Sharp, and R. R. Neurgaonkar, Phys. Rev. Lett. 71, 553 (1993).

J. Comput. Phys. (1)

T. P. Taha and M. J. Ablowitz, J. Comput. Phys. 55, 203 (1984).

J. Opt. Soc. Am. B (5)

Opt. Commun. (3)

L. Poladian, A. W. Snyder, and D. J. Mitchell, Opt. Commun. 85, 59 (1991).

G. Leo, G. Assanto, and W. E. Torruellas, Opt. Commun. 134, 223 (1997).

V. V. Steblina, Yu. S. Kivshar, M. Lisak, and B. A. Malomed, Opt. Commun. 118, 345 (1995).

Opt. Lett. (11)

Opt. Quantum Electron. (1)

G. I. Stegeman, D. J. Hagan, and L. Torner, Opt. Quantum Electron. 28, 1691 (1996).

Phys. Lett. A (1)

A. V. Buryak and Yu. S. Kivshar, Phys. Lett. A 197, 407 (1995).

Phys. Rev. A (3)

C. Etrich, U. Peschel, F. Lederer, and B. Malomed, Phys. Rev. A 52, R3444 (1995).

A. V. Buryak, Yu. S. Kivshar, and V. V. Steblina, Phys. Rev. A 52, 1670 (1995).

D. E. Edmundson and R. H. Enns, Phys. Rev. A 51, 2491 (1995).

Phys. Rev. E (1)

B. Malomed, P. Drummond, H. He, A. Berntson, D. Anderson, and M. Lisak, Phys. Rev. E 56, 4725 (1997).

Phys. Rev. Lett. (6)

A. V. Buryak, Yu. S. Kivshar, and S. Trillo, Phys. Rev. Lett. 77, 5210 (1996).

A. V. Buryak and Yu. S. Kivshar, Phys. Rev. Lett. 78, 3286 (1997).

V. Tikhonenko, J. Christou, and B. Luther-Davies, Phys. Rev. Lett. 76, 2698 (1996).

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. Van Stryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, Phys. Rev. Lett. 74, 5036 (1995).

G. C. Duree, J. L. Shultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. Di Porto, E. J. Sharp, and R. R. Neurgaonkar, Phys. Rev. Lett. 71, 553 (1993).

D. E. Pelinovsky, A. V. Buryak, and Yu. S. Kivshar, Phys. Rev. Lett. 75, 591 (1995).

Phys. Today (1)

M. Segev and G. I. Stegeman, Phys. Today 51, 42 (1998), and references therein.

Physica D (2)

K. A. Gorshkov and L. A. Ostrovsky, Physica D 3, 428 (1981).

V. I. Karpman and V. V. Solov’ev, Physica D 3, 487 (1981).

Other (4)

M. Shih, M. Segev, and G. Salamo, Phys. Rev. Lett. 78, 2551 (1997); A. V. Buryak, Yu. S. Kivshar, M. Shih, and M. Segev, Phys. Rev. Lett. (to be published).

A. V. Buryak, “Solitons due to second harmonic generation,” Ph.D. dissertation (Australian National University, Canberra, 1996).

C. Etrich, U. Peschel, F. Lederer, B. Malomed, and Yu. S. Kivshar, Phys. Rev. E 54, 4321 (1996); D. E. Pelenovsky, Yu. S. Kivshar, and V. V. Afanasjev, Physica D 116, 121 (1998); Yu. S. Kivshar, D. E. Pelenovsky, T. Cretegny, and M. Peyrard, Phys. Rev. Lett. PRLTAO 80, 5032 (1998).

H. Goldstein, Classical Mechanics (Addison-Wesley, Reading, Mass., 1980), Chap. 3.

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