Application of the inverse scattering transform method to SBBS in an inhomogeneous medium: the Zakharov–Manakov solution

1983 ◽  
Vol 61 (4) ◽  
pp. 604-611 ◽  
Author(s):  
R. H. Enns
Keyword(s):  
Inhomogeneous Medium ◽  
Inverse Scattering ◽  
Temporal Evolution ◽  
Inverse Scattering Transform ◽  
Experimental Setup ◽  
Transform Method ◽  
Light Pulses ◽  
Spatially Inhomogeneous ◽  
Scattering Transform ◽  
Stimulated Brillouin

The inverse scattering transform method has been applied to the stimulated Brillouin backscattering (SBBS) interaction in a weakly spatially inhomogeneous medium. Specifically, the Zakharov–Manakov problem has been solved for examples of both an amplifier and a generator experimental setup yielding the complete spatial and temporal evolution of the light pulses involved. The structure of the resulting pulse shapes is discussed and the results compared with those in the literature.

Zakharov–Manakov solution of the 3-wave explosive interaction problem

1983 ◽  
Vol 61 (10) ◽  
pp. 1386-1400 ◽  
Author(s):  
R. H. Enns ◽  
S. S. Rangnekar
Keyword(s):  
Inverse Scattering ◽  
Temporal Evolution ◽  
Inverse Scattering Transform ◽  
Transform Method ◽  
Scattering Transform ◽  
Interaction Problem

The inverse scattering transform method has been applied to the on-resonance 3-wave explosive interaction problem. In particular, the Zakharov–Manakov problem has been solved to yield the complete spatial and temporal evolution of the envelopes of the three waves involved. A comparison with numerically derived envelope shapes is made and the results are discussed.

Application of the inverse scattering transform method to stimulated Brillouin backscattering in a generator setup: The Zakharov–Manakov solution

1981 ◽  
Vol 59 (12) ◽  
pp. 1817-1828 ◽  
Author(s):  
S. S. Rangnekar ◽  
R. H. Enns
Keyword(s):  
Laser Pulse ◽  
Numerical Integration ◽  
Inverse Scattering ◽  
Inverse Scattering Transform ◽  
Transform Method ◽  
Scattering Transform ◽  
Direct Numerical Integration ◽  
Stimulated Brillouin

Making use of the inverse scattering transform method (ISTM), we have solved the Zakharov–Manakov problem for the stimulated Brillouin backscattering (SBBS) of a laser pulse by a fluctuation, the envelopes of both being rectangular. The results are consistent with those obtained by Kaup and co-workers using a combination of direct numerical integration and Zakharov–Shabat analysis.

Zakharov–Manakov solution of the stimulated Brillouin backscattering generator problem for non-rectangular envelopes

1982 ◽  
Vol 60 (10) ◽  
pp. 1404-1413 ◽  
Author(s):  
R. H. Enns
Keyword(s):  
Laser Pulse ◽  
Inverse Scattering ◽  
Inverse Scattering Transform ◽  
Transform Method ◽  
Scattering Transform ◽  
Stimulated Brillouin

Making use of the inverse scattering transform method (ISTM), we have solved the Zakharov–Manakov problem for the stimulated Brillouin backscattering of a laser pulse by an acoustic fluctuation for a situation where the envelopes are non-rectangular. We have chosen input potentials which simulate rapidly rising pulses with exponentially decaying tails. The extension of the analysis to other input shapes is discussed.

Zakharov–Manakov solution of the stimulated Brillouin backscattering generator problem for "spliced" potentials

1982 ◽  
Vol 60 (11) ◽  
pp. 1620-1629 ◽  
Author(s):  
R. H. Enns
Keyword(s):  
Light Scattering ◽  
Eigenvalue Problem ◽  
Series Solution ◽  
Inverse Scattering Transform ◽  
Experimental Conditions ◽  
Transform Method ◽  
Scattering Transform ◽  
Exactly Solvable ◽  
Nonlinear Light Scattering ◽  
Stimulated Brillouin

Making use of the inverse scattering transform method (ISTM), one would like to solve the Zakharov–Manakov (Z–M) problem relevant to nonlinear light scattering for "realistic" nonrectangular input shapes, i.e., shapes which might simulate actual experimental conditions. One approach, which is illustrated in this paper with a specific simple example, is to "splice" potentials together, using potentials for which the Z–M eigenvalue problem is exactly solvable in terms of known functions. A table of such potentials discovered to date is presented. An alternate approach, which avoids splicing, but involves seeking a series solution to the Z–M eigenvalue problem is also briefly discussed.

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