Self-focusing with fourth-order dispersion

SIAM Journal on Applied Mathematics

Volumn 62, Issue 4, 2002, Pages 1437-1462

  Fibich, Gadi ^a   Ilan, Boaz ^a   Papanicolaou, George ^a  

^a TEL AVIV UNIVERSITY   (Israel)

Author keywords

Blowup; Critical exponent; Critical power; Gagliardo Nirenberg inequality; Optimal constants

Indexed keywords

DISPERSION (WAVES); ELECTROMAGNETIC WAVE PROPAGATION; FIBER LASERS; MATHEMATICAL MODELS; OPTIMIZATION;

FIBER ARRAYS; FOURTH ORDER DISPERSION; GAGLIARDO-NIRENBERG INEQUALITY; ISOTROPIC MIXED DISPERSION; NONISOTROPIC MIXED DISPERSION; NONLINEAR SCHRODINGER EQUATION;

NONLINEAR EQUATIONS;

EID: 0036552454     PISSN: 00361399     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036139901387241     Document Type: Article

References (33)

1. All-optical-switching and pulse amplification and steering in nonlinear fiber arrays
2. Multidimensional solitons in fiber arrays
3. Energy localization in nonlinear fiber arrays: Collapse effect compressor
4. Optical pulse compression using fiber arrays
5. Generation of a train of three-dimensional optical solitons in a self-focusing medium
6. Dispersion estimates for fourth order Schrödinger equations
7. Vector theory of self-focusing of an optical beam in Kerr media
8. Beam nonparaxiality, filament formation, and beam breakup in the self-focusing of optical beams
9. Small beam nonparaxiality arrests self-focusing of optical beams
10. Self-focusing in the damped nonlinear Schrödinger equation
11. Critical power for self-focusing in bulk media and in hollow waveguides
12. Vectorial and random effects in self-focusing and in multiple filamentation
13. Vectorial effects in self-focusing and multiple filamentation
14. Self-focusing in the perturbed and unperturbed nonlinear Schrödinger equation in critical dimension
15. A modulation method for self-focusing in the perturbed critical nonlinear Schrödinger equation
16. High-order two-way artificial boundary conditions for nonlinear wave propagation with backscattering
17. Proprieta di alcune classi di funzioni in piu varibili
18. Ulteriora proprieta di alcune classi di funzioni in piu varibili
19. On a class of nonlinear Schrödinger equations. I: The cauchy problem, general case
20. Stable three-dimensional small-amplitude soliton in magnetic materials
21. Stability of solitons described by nonlinear Schrödinger-type equations with higher-order dispersion
22. On nonlinear Schrödinger equations
23. n
24. Analytic criterion for soliton instability in a nonlinear fiber array
25. Stability and instability of fourth-order solitary waves
26. On the analytical theory for stationary self-focusing of radiation
27. 2 concentration of blow-up solutions for the nonlinear Schrödinger equation with critical power nonlinearity
28. On elliptic partial differential equations
29. Description of the self-focusing and collapse effects by a modified nonlinear Schrödinger equation
30. Three-dimensional dispersion of nonlinearity and stability of multidimensional solitons
31. Nonlinear Schrödinger equations and sharp interpolation estimates
32. Excitation and dynamics of pulses in coupled fiber arrays