scholarly journals Existence of Global Solutions to the Derivative NLS Equation with the Inverse Scattering Transform Method

2017 ◽  
Vol 2018 (18) ◽  
pp. 5663-5728 ◽  
Author(s):  
Dmitry E Pelinovsky ◽  
Yusuke Shimabukuro
Keyword(s):  
Inverse Scattering ◽  
Global Solutions ◽  
Inverse Scattering Transform ◽  
Nls Equation ◽  
Transform Method ◽  
Scattering Transform

Inverse Scattering Transform Method

1999 ◽  
pp. 107-132
Author(s):  
A. I. Maimistov ◽  
A. M. Basharov
Keyword(s):  
Inverse Scattering ◽  
Inverse Scattering Transform ◽  
Transform Method ◽  
Scattering Transform

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.

scholarly journals Stability of multi-solitons in the cubic NLS equation

2014 ◽  
Vol 11 (02) ◽  
pp. 329-353 ◽  
Author(s):  
Andres Contreras ◽  
Dmitry Pelinovsky
Keyword(s):  
Initial Data ◽  
Inverse Scattering ◽  
Orbital Stability ◽  
Inverse Scattering Transform ◽  
Nls Equation ◽  
Transform Methods ◽  
Nonlinear Schrödinger ◽  
Scattering Transform ◽  
The Stability

We address the stability of multi-solitons for the cubic nonlinear Schrödinger (NLS) equation on the line. By using the dressing transformation and the inverse scattering transform methods, we establish the orbital stability of multi-solitons in the L2(ℝ) space when the initial data is in a weighted L2(ℝ) space.

scholarly journals Prolongation Structures and N-Soliton Solutions for a New Nonlinear Schrödinger-Type Equation via Riemann-Hilbert Approach

2019 ◽  
Vol 2019 ◽  
pp. 1-10 ◽  
Author(s):  
Yuxin Lin ◽  
Yong Fang ◽  
Huanhe Dong
Keyword(s):  
Spectral Problem ◽  
Inverse Scattering ◽  
Soliton Solutions ◽  
Type Equation ◽  
Lax Pair ◽  
Inverse Scattering Transform ◽  
Nls Equation ◽  
Nonlinear Schrödinger ◽  
Scattering Transform ◽  
Matrix Spectral Problem

In this paper, a new integrable nonlinear Schrödinger-type (NLST) equation is investigated by prolongation structures theory and Riemann-Hilbert (R-H) approach. Via prolongation structures theory, the Lax pair of the NLST equation, a 2×2 matrix spectral problem, is derived. Depending on the analysis of red the spectral problem, a R-H problem of the NLST equation is formulated. Furthermore, through a specific R-H problem with the vanishing scattering coefficient, N-soliton solutions of the NLST equation are expressed explicitly. Moreover, a few key differences are presented, which exist in the implementation of the inverse scattering transform for NLST equation and cubic nonlinear Schrödinger (NLS) equation. Finally, the dynamic behaviors of soliton solutions are shown by selecting appropriate spectral parameter λ, respectively.

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