Instabilities in the two-dimensional cubic nonlinear Schrödinger equation

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 68, Issue 4 2, 2003, Pages 456011-456014

  Carter, John D ^a   Segur, Harvey ^b  

^a SEATTLE UNIVERSITY   (United States)

^b UNIVERSITY OF COLORADO   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ASYMPTOTIC STABILITY; BOUNDARY CONDITIONS; HAMILTONIANS; LINEARIZATION; NONLINEAR EQUATIONS; NUMERICAL METHODS; PERTURBATION TECHNIQUES; PHASE SPACE METHODS; PROBLEM SOLVING; WAVE PROPAGATION;

SCHRODINGER EQUATIONS; TRAVELING WAVES; WAVE NUMBERS;

WAVE EQUATIONS;

EID: 0346305003     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (25)

1. S.V. Manakov, Zh. Eksp. Teor. Fiz. 65, 505 (1973) [Sov. Phys. JETP 38, 248 (1974)].
2. S.V. Manakov, Zh. Eksp. Teor. Fiz. 65, 505 (1973) [Sov. Phys. JETP 38, 248 (1974)].
3. D.J. Benney and G.J. Roskes, Stud. Appl. Math. 48, 377 (1969).
4. A. Davey and K. Stewartson, Proc. R. Soc. London, Ser. A 38, 101 (1974).
5. H.L. Pecseli, IEEE Trans. Plasma Sci. 13, 53 (1985).
6. R. Donnelly, Quantized Vortices in Helium II (Cambridge University, London, England, 1991).
7. E.P. Gross, J. Math. Phys. 4, 195 (1963).
8. L.P. Pitaevskii, Zh. Eksp. Teor. Fiz. 40, 646 (1961) [Sov. Phys. JETP 13, 451 (1961)].
9. L.P. Pitaevskii, Zh. Eksp. Teor. Fiz. 40, 646 (1961) [Sov. Phys. JETP 13, 451 (1961)].
10. P. L. Sulem and C. Sulem, Nonlinear Schrödinger Equations: Self-focusing and Wave Collapse (Springer, New York, 1999).
11. P. F. Byrd and M. D. Friedman, Handbook of Elliptic Integrals for Engineers and Physicists (Springer-Verlag, Berlin, 1954).
12. L.D. Carr, C.W. Clark, and W.P. Reinhardt, Phys. Rev. A 62, 063610 (2000); 62, 063611 (2000).
13. L.D. Carr, C.W. Clark, and W.P. Reinhardt, Phys. Rev. A 62, 063610 (2000); 62, 063611 (2000).
14. V.E. Zakharov and A.M. Rubenchik, Sov. Phys. JETP 38, 494 (1974).
15. D.E. Pelinovsky, Math. Comput. Simul. 55, 585 (2001).
16. E.A. Kuznetsov et al., Phys. Rep. 142, 103 (1986).
17. K. Rypdal and J.J. Rasmussen, Phys. Scr. 40, 192 (1989).
18. Y.S. Kivshar and D.E. Pelinovsky, Phys. Rep. 331, 117 (2000).
19. D.U. Martin, H.C. Yuen, and P.G. Saffman, Wave Motion 2, 215 (1980).
20. E. Infeld and J. Ziemkiewicz, Acta Phys. Pol. A 59, 255 (1981).
21. V.A. Aleshkevich et al., Phys. Rev. E 67, 066605 (2003).
22. Y.V. Kartashov et al., J. Opt. Soc. Am. B 20, 1273 (2003).
23. J. D. Carter, Ph.D. thesis, University of Colorado, 2001.
24. R. B. Guenther and J. W. Lee, Partial Differential Equations of Mathematical Physics and Integral Equations (Prentice Hall, Englewood Cliffs, NJ, 1988).
25. K. R. Meyer and G. R. Hall, Introduction to the Theory of Hamiltonian Systems (Springer-Verlag, Berlin, 1992).