Scattering transform for nonstationary Schrödinger equation with bidimensionally perturbed N-soliton potential

M. Boiti; F. Pempinelli; A. K. Pogrebkov

doi:10.1063/1.2393144

Scattering transform for nonstationary Schrödinger equation with bidimensionally perturbed N-soliton potential

Journal of Mathematical Physics ◽

10.1063/1.2393144 ◽

2006 ◽

Vol 47 (12) ◽

pp. 123510 ◽

Cited By ~ 10

Author(s):

M. Boiti ◽

F. Pempinelli ◽

A. K. Pogrebkov

Keyword(s):

Schrödinger Equation ◽

Schrodinger Equation ◽

Scattering Transform ◽

Nonstationary Schrödinger Equation

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Triple-pole soliton solutions of the derivative nonlinear Schrödinger equation via inverse scattering transform

Applied Mathematics Letters ◽

10.1016/j.aml.2021.107741 ◽

2021 ◽

pp. 107741

Author(s):

Nan Liu ◽

Zuxing Xuan ◽

Jinyi Sun

Keyword(s):

Schrödinger Equation ◽

Inverse Scattering ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Soliton Solutions ◽

Inverse Scattering Transform ◽

Nonlinear Schrodinger Equation ◽

Nonlinear Schrödinger ◽

Scattering Transform ◽

Derivative Nonlinear Schrödinger Equation

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Family of finite-difference schemes with approximate transparent boundary conditions for the generalized nonstationary Schrödinger equation in a semi-infinite strip

Computational Mathematics and Mathematical Physics ◽

10.1134/s0965542511030122 ◽

2011 ◽

Vol 51 (3) ◽

pp. 355-376 ◽

Cited By ~ 8

Author(s):

I. A. Zlotnik

Keyword(s):

Finite Difference ◽

Schrödinger Equation ◽

Boundary Conditions ◽

Schrodinger Equation ◽

Difference Schemes ◽

Finite Difference Schemes ◽

Infinite Strip ◽

Transparent Boundary Conditions ◽

Nonstationary Schrödinger Equation

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Inverse Scattering Transform for the Focusing Nonlinear Schrödinger Equation with a One-Sided Non-Zero Boundary Condition

Algebraic and Analytic Aspects of Integrable Systems and Painlevé Equations - Contemporary Mathematics ◽

10.1090/conm/651/13035 ◽

2015 ◽

pp. 157-194 ◽

Cited By ~ 8

Author(s):

B. Prinari ◽

F. Vitale

Keyword(s):

Boundary Condition ◽

Schrödinger Equation ◽

Inverse Scattering ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Inverse Scattering Transform ◽

Nonlinear Schrodinger Equation ◽

Nonlinear Schrödinger ◽

Scattering Transform

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On linear similarity of certain nonselfadjoint operators to selfadjoint operators and on the asymptotic behavior for 𝑡→∞ of the solution of a nonstationary Schrödinger equation

Thirteen Papers on Functional Analysis and Differential Equations - American Mathematical Society Translations: Series 2 ◽

10.1090/trans2/079/06 ◽

1968 ◽

pp. 97-150 ◽

Cited By ~ 1

Author(s):

I. V. Stankevič

Keyword(s):

Asymptotic Behavior ◽

Schrödinger Equation ◽

Schrodinger Equation ◽

Selfadjoint Operators ◽

Nonstationary Schrödinger Equation

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Optimal control problem for nonstationary Schrödinger equation

Numerical Methods for Partial Differential Equations ◽

10.1002/num.20395 ◽

2009 ◽

Vol 25 (5) ◽

pp. 1195-1203 ◽

Cited By ~ 3

Author(s):

Bunyamin Yildiz ◽

Oguz Kilicoglu ◽

G. Yagubov

Keyword(s):

Optimal Control ◽

Schrödinger Equation ◽

Optimal Control Problem ◽

Control Problem ◽

Schrodinger Equation ◽

Nonstationary Schrödinger Equation

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Inverse scattering transform for the defocusing nonlinear Schrödinger equation with fully asymmetric non-zero boundary conditions

Physica D Nonlinear Phenomena ◽

10.1016/j.physd.2016.04.003 ◽

2016 ◽

Vol 333 ◽

pp. 117-136 ◽

Cited By ~ 12

Author(s):

Gino Biondini ◽

Emily Fagerstrom ◽

Barbara Prinari

Keyword(s):

Schrödinger Equation ◽

Boundary Conditions ◽

Inverse Scattering ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Inverse Scattering Transform ◽

Nonlinear Schrodinger Equation ◽

Nonlinear Schrödinger ◽

Scattering Transform

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Exact solutions of the nonstationary Schrödinger equation

Theoretical and Mathematical Physics ◽

10.1007/bf02557214 ◽

1999 ◽

Vol 121 (3) ◽

pp. 1700-1700

Author(s):

E. P. Velicheva ◽

A. A. Suz'ko

Keyword(s):

Schrödinger Equation ◽

Exact Solutions ◽

Schrodinger Equation ◽

Nonstationary Schrödinger Equation

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Inverse scattering transform for the time dependent Schrödinger equation with applications to the KPI equation

Communications in Mathematical Physics ◽

10.1007/bf02096873 ◽

1990 ◽

Vol 128 (3) ◽

pp. 551-564 ◽

Cited By ~ 46

Author(s):

Xin Zhou

Keyword(s):

Schrödinger Equation ◽

Inverse Scattering ◽

Schrodinger Equation ◽

Inverse Scattering Transform ◽

Time Dependent ◽

Scattering Transform

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Inverse scattering transform for the integrable nonlocal nonlinear Schrödinger equation

Nonlinearity ◽

10.1088/0951-7715/29/3/915 ◽

2016 ◽

Vol 29 (3) ◽

pp. 915-946 ◽

Cited By ~ 196

Author(s):

Mark J Ablowitz ◽

Ziad H Musslimani

Keyword(s):

Schrödinger Equation ◽

Inverse Scattering ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Inverse Scattering Transform ◽

Nonlinear Schrodinger Equation ◽

Nonlinear Schrödinger ◽

Scattering Transform ◽

Nonlocal Nonlinear Schrödinger Equation ◽

Nonlocal Nonlinear

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Sobolev mapping properties of the scattering transform for the Schrödinger equation

Contemporary Mathematics - Spectral Theory and Geometric Analysis ◽

10.1090/conm/535/10536 ◽

2011 ◽

pp. 79-93 ◽

Cited By ~ 1

Author(s):

Rostyslav Hryniv ◽

Yaroslav Mykytyuk ◽

Peter Perry

Keyword(s):

Schrödinger Equation ◽

Schrodinger Equation ◽

Sobolev Mapping ◽

Scattering Transform

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