Bäcklund Transformations for the One-Dimensional Schrödinger Equation

被引：0

作者：

Neshchadim M.V. ^{[1
,2
]}

机构：

[1] Sobolev Institute of Mathematics, Novosibirsk

[2] Novosibirsk State University, Novosibirsk

来源：

Journal of Applied and Industrial Mathematics | 2021年 / 15卷 / 02期

关键词：

Bäcklund transformation; compatibility condition; Schrödinger equation;

D O I：

10.1134/S1990478921020125

中图分类号：

学科分类号：

摘要：

Abstract: We study the system of equations which bases on the one-dimensionalSchrödinger equation and connects the potential, amplitude, and phase functions. Usingthe methods of compatibility theory of systems of partial differential equations, we obtain thecompletely integrable systems that connect only two functions of the above three. As a corollary,we construct some exact solutions of the Schrödinger equation. © 2021, Pleiades Publishing, Ltd.

引用

页码：307 / 314

页数：7

共 50 条

[41] Transmission coefficient for excitations passing through a one-dimensional barrier described by the nonlinear Schrödinger equation
D. L. Kovrizhin
L. A. Maksimov
[J]. Doklady Physics, 2001, 46 : 328 - 330
[42] Existence of a solution to the inhomogeneous equation with the one-dimensional Schrödinger operator in the space of quickly decreasing functions
Valerii Samoylenko
Yuliya Samoylenko
[J]. Journal of Mathematical Sciences, 2012, 187 (1) : 70 - 76
[43] Finite element method with discrete transparent boundary conditions for the one-dimensional nonstationary Schrödinger equation
A. A. Zlotnik
I. A. Zlotnik
[J]. Doklady Mathematics, 2012, 86 : 750 - 755
[44] High-order multiscale discontinuous Galerkin methods for the one-dimensional stationary Schrödinger equation
Dong, Bo
Wang, Wei
[J]. Journal of Computational and Applied Mathematics, 2021, 380
[45] On the spectral investigation of the scattering problem for some version of one-dimensional Schrödinger equation with turning point
Zaki FA El-Raheem
AH Nasser
[J]. Boundary Value Problems, 2014
[46] Hamiltonian of the One-Dimensional Torsion Schrödinger Equation in a Complex-Valued Basis of Mathieu Functions
A. N. Belov
V. V. Turovtsev
Yu. D. Orlov
[J]. Russian Physics Journal, 2017, 60 : 928 - 934
[47] Exponential Relaxation to Equilibrium for a One-Dimensional Focusing Non-Linear Schrödinger Equation with Noise
Eric A. Carlen
Jürg Fröhlich
Joel Lebowitz
[J]. Communications in Mathematical Physics, 2016, 342 : 303 - 332
[48] Generalized Lyapunov exponent for the one-dimensional Schr?dinger equation with Cauchy disorder: Some exact results
Comtet, Alain
Texier, Christophe
Tourigny, Yves
[J]. PHYSICAL REVIEW E, 2022, 105 (06)
[49] Fast evaluation of exact transparent boundary condition for one-dimensional cubic nonlinear Schrödinger equation
Chunxiong Zheng
[J]. Frontiers of Mathematics in China, 2010, 5 : 589 - 606
[50] Semiclassical, trajectory-coherent, quasi-energy states for the one-dimensional schrödinger equation
Baranov V.D.
Belov V.V.
Trifonov A.Yu.
[J]. Russian Physics Journal, 2000, 43 (1) : 1 - 5

← 1 2 3 4 5 →