The inverse scattering transform for solving the discrete sine-Gordon equation

1982 ◽  
Vol 92 (1) ◽  
pp. 5-8 ◽  
Author(s):  
L. Pilloni ◽  
D. Levi
Keyword(s):  
Inverse Scattering ◽  
Gordon Equation ◽  
Inverse Scattering Transform ◽  
Sine Gordon Equation ◽  
Scattering Transform

An inverse scattering study of the radiation solution of the sine–Gordon equation

1984 ◽  
Vol 62 (7) ◽  
pp. 701-713
Author(s):  
R. H. Enns ◽  
S. S. Rangnekar
Keyword(s):  
Inverse Scattering ◽  
Evolution Equations ◽  
Gordon Equation ◽  
Wave Interaction ◽  
Nonlinear Evolution Equations ◽  
Sine Gordon Equation ◽  
Transform Method ◽  
Scattering Transform ◽  
Scattering Study ◽  
Interaction Problem

Making use of the diagrammatic approach to the inverse scattering transform method that we pioneered on the 3-wave interaction problem, we have studied the complete temporal and spatial evolution of the radiation solution of the sine–Gordon equation. The analytic results are consistent with numerical simulations as well as qualitative ideas prevalent in the literature. The extension of the diagrammatic approach to the sinh–Gordon and other nonlinear evolution equations of physical significance is also briefly discussed.

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