Multiple solitary waves due to second-harmonic generation in quadratic media

Journal of Nonlinear Science

Volumn 9, Issue 1, 1999, Pages 33-52

  Yew, A C ^a   Champneys, A R ^b   McKenna, P J ^c  

^a BROWN UNIVERSITY   (United States)

^b UNIVERSITY OF BRISTOL   (United Kingdom)

^c UNIVERSITY OF CONNECTICUT   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0010904761     PISSN: 09388974     EISSN: None     Source Type: Journal    
DOI: 10.1007/s003329900063     Document Type: Article

References (21)

1. Werner, M. J., & Drummond, P. D., Simulton solutions for the parametric-amplifier. J. Opt. Soc. Am. B 10 (1993) 2390-2393.
2. (2) cascading. J. Opt. Soc. Am. B11 (1994) 2434-2443.
3. Buryak, A. V., & Kivshar, Yu. S., Solitons due to second harmonic generation. Phys. Lett. A 197 (1995) 407-412.
4. Claussen, C. B., Bang, O., & Kivshar, Y. S., Spatial solitons and induced Kerr effects in quasi-phase-matched quadratic media. Phys. Rev. Lett. 78 (1997) 4749-4752.
5. He, H., Werner, M. J., & Drummond, P. D., Simultaneous solitary-wave solutions in a non-linear parametric waveguide. Phys. Rev. E 54 (1996) 896-911.
6. Karamzin, Y. N., & Sukhorukov, A. P., Nonlinear interaction of diffracted light beams in a medium with quadratic nonlinearity: mutual focusing of beams and limitation on the efficiency of optical frequency converters. JETP Lett. 20 (1974) 339-342.
7. Mihalache, D., Lederer, F., Mazilu, D., & Crasovan, L.-C., Multiple-humped bright solitary waves in second-order nonlinear media. Opt. Eng. 35 (1996) 1616-1623.
8. Haelterman, M., Trillo, S., & Ferro, P., Multiple soliton bound states and symmetry breaking in quadratic media. Opt. Lett. 22 (1997) 84-86.
9. Lions, P.-L., The concentration-compactness principle in the calculus of variations: the locally compact case. Ann. Inst. H. Poincaré, Anal. Non-linéaire 1 (1984) 109-145, 223-283.
10. Lions, P.-L., The Coconcentration-compactness principle in the calculus of variations: the limit case. Rev. Mat. Iberoamericana 1.1 (1985) 145-201, 1.2 45-121.
11. Struwe, M., Variational Methods: Applications to Nonlinear Partial Differential Equations and Hamiltonian Systems. Springer-Verlag: New York, 1990, 1996.
12. Chen, Y., & McKenna, P. J., Travelling waves in a nonlinearly suspended beam: Theoretical results and numerical observations. J. Diff. Eqns. 136 (1997) 325-355.
13. Buffoni, B., & Séré, E., A global condition for quasi-random behavior in a class of conservative systems. Commun. Pure Appl. Math. 49 (1996) 285-305.
14. Rabinowitz, P. H., Minimax methods in critical point theory with applications to differential equations. CBMS Regional Conference Series in Mathematics, Vol. 65. American Mathematical Society: Providence, RI, 1986.
15. p approach to the Dirichlet problem. Ann. Scuola Norm. Sup. Pisa 13 (1959) 405-448.
16. Renardy, M., & Rogers, R. C., An Introduction to Partial Differential Equations, Chapter 6. Texts in Applied Mathematics 13. Springer-Verlag: New York, 1993.
17. Hutson, V., & Pym, J. S., Applications of Functional Analysis and Operator Theory. Academic Press: New York, 1980.
18. Champneys, A. R., & Spence, A., Hunting for homoclinic orbits in reversible systems: A shooting technique. Adv. Comp. Math. 1 (1993) 81-108.
19. Doedel, E. J., Keller, H. B., & Kernévez, J. P., Numerical analysis and control of bifurcation problems. Int. J. Bifurcation & Chaos 1 (1991) 493-520, 745-772.
20. Sandstede, B., Verzweigungstheorie homokliner Verdopplungen. Doctoral thesis, University of Stuttgart (1993).
21. Lin, X.-B., Using Melnikov's method to solve Silnikov's problems. Proc. Roy. Soc. Edinburgh, 116A (1990), 295-325.