The scattering problem for the Schr�dinger equation with a potential linear in time and in space. II. Correctness, smoothness, behavior of the solution at infinity

1987 ◽  
Vol 38 (1) ◽  
pp. 1562-1576 ◽  
Author(s):  
V. M. Babich ◽  
V. P. Smyshlyaev
Keyword(s):  
Scattering Problem ◽  
Dinger Equation

scholarly journals Scattering Problem for the Supercritical Nonlinear Schrödinger Equation in 1d

2015 ◽  
Vol 58 (3) ◽  
pp. 451-470
Author(s):  
Nakao Hayashi ◽  
Pavel I. Naumkin
Keyword(s):  
Scattering Problem ◽  
Dinger Equation

scholarly journals The relation of Zakharov-Shabat scattering problem to Schrödinger equation with complex potential and approximations for soliton parameters

2019 ◽  
Vol 65 (6 Nov-Dec) ◽  
pp. 634
Author(s):  
N. Korneev ◽  
J. A. Catana ◽  
V. A. Vyslooukh
Keyword(s):  
Schrödinger Equation ◽  
High Power ◽  
Complex Potential ◽  
Schrodinger Equation ◽  
Scattering Problem ◽  
Dinger Equation ◽  
Kerr Media ◽  
Different Types

The relation of Zakharov-Shabat scattering problem to Schr\"{o}dinger equation with complex potential is used to analytically approximate parameters of high power solitons produced in positive Kerr media with chirped parabolic pulses. The soliton parameters are estimated for different types of chirp and intensity distortions. The comparison with numerics is discussed.

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