On a non-local formulation of the inverse scattering transform method

1985 ◽  
Vol 1 (4) ◽  
pp. L29-L33
Author(s):  
B G Konopelchenko
Keyword(s):  
Inverse Scattering ◽  
Inverse Scattering Transform ◽  
Transform Method ◽  
Scattering Transform ◽  
Non Local

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.

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