On the proof of the absence of renormalization of the constant in the vector-variant of β-interaction

1958 ◽  
Vol 10 (2) ◽  
pp. 352-354 ◽  
Author(s):  
B. L. Ioffe
Keyword(s):  
Vector Variant

Algorithms for solving scattering problems for the Manakov model of nonlinear Schrödinger equations

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Leonid L. Frumin
Keyword(s):  
Scattering Problem ◽  
Inverse Scattering Problem ◽  
Numerical Algorithms ◽  
Scattering Problems ◽  
Block Matrices ◽  
Nonlinear Schrödinger ◽  
Direct Scattering ◽  
Vector Case ◽  
Manakov Model ◽  
Vector Variant

AbstractWe introduce numerical algorithms for solving the inverse and direct scattering problems for the Manakov model of vector nonlinear Schrödinger equation. We have found an algebraic group of 4-block matrices with off-diagonal blocks consisting of special vector-like matrices for generalizing the scalar problem’s efficient numerical algorithms to the vector case. The inversion of block matrices of the discretized system of Gelfand–Levitan–Marchenko integral equations solves the inverse scattering problem using the vector variant the Toeplitz Inner Bordering algorithm of Levinson’s type. The reversal of steps of the inverse problem algorithm gives the solution of the direct scattering problem. Numerical tests confirm the proposed vector algorithms’ efficiency and stability. We also present an example of the algorithms’ application to simulate the Manakov vector solitons’ collision.

Vector variant of the Adamyan—Arov—Krein theorem

1986 ◽  
Vol 20 (1) ◽  
pp. 74-76 ◽  
Author(s):  
S. R. Treil’
Keyword(s):  
Krein Theorem ◽  
Vector Variant
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