On the Inverse Scattering Problem for the One-Dimensional Schrodinger Equation with Increasing Potential

被引：1

作者：

Guseinov, I. M. ^{[1
,2
,3
]}

Khanmamedov, Ag. Kh. ^{[1
,2
,3
]}

机构：

[1] Baku State Univ, Baku, Azerbaijan

[2] Azerbaijan Univ, Azerbaijan Natl Acad Sci, Inst Math & Mech, Baku, Azerbaijan

[3] Azerbaijan Univ, Baku, Azerbaijan

来源：

UKRAINIAN MATHEMATICAL JOURNAL | 2019年 / 70卷 / 10期

关键词：

D O I：

10.1007/s11253-019-01593-z

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider a one-dimensional Schrodinger equation on the entire axis whose potential rapidly decreases on the left-hand side and infinitely increases on the right-hand side. By the method of transformation operators, we study the inverse scattering problem. We establish conditions for the scattering data under which the inverse problem is solvable. The main Marchenko-type integral equations are investigated and their unique solvability is established.

引用

页码：1604 / 1618

页数：15

共 50 条

[1] THE ONE-DIMENSIONAL INVERSE SCATTERING PROBLEM FOR AN INCREASING POTENTIAL
KRISTENSSON, G
[J]. JOURNAL OF MATHEMATICAL PHYSICS, 1986, 27 (03) : 804 - 815
[2] On the Inverse Scattering Problem for the One-Dimensional Schrödinger Equation with Increasing Potential
I. M. Guseinov
Ag. Kh. Khanmamedov
[J]. Ukrainian Mathematical Journal, 2019, 70 : 1604 - 1618
[3] Inverse problem of scattering theory for a class one-dimensional Schrodinger equation
Mamedov, Kh R.
Nabiev, A. A.
[J]. QUAESTIONES MATHEMATICAE, 2019, 42 (07) : 841 - 856
[4] Inverse Scattering Problem for One-Dimensional Schrodinger Equation with Discontinuity Conditions
Huseynov, H. M.
Osmanli, J. A.
[J]. JOURNAL OF MATHEMATICAL PHYSICS ANALYSIS GEOMETRY, 2013, 9 (03) : 332 - 359
[5] ON THE INVERSE SCATTERING PROBLEM FOR THE ONE-DIMENSIONAL SCHRODINGER-EQUATION WITH AN ENERGY-DEPENDENT POTENTIAL
TSUTSUMI, M
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1981, 83 (01) : 316 - 350
[6] INVERSE SPECTRAL PROBLEM FOR ONE-DIMENSIONAL SCHRODINGER EQUATION WITH AN ADDITIONAL LINEAR POTENTIAL
CALOGERO, F
DEGASPERIS, A
[J]. LETTERE AL NUOVO CIMENTO, 1978, 23 (04): : 143 - 149
[7] Direct and inverse scattering on the line for one-dimensional Schrodinger equation
Bazargan, J.
[J]. PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY, 2007, (03): : 245 - 248
[8] Scattering Matrix of the One-Dimensional Schrodinger Equation with Arbitrary Potential
Ramirez, Carlos
Leon, Rodrigo
[J]. JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN, 2017, 86 (11)
[9] INVERSE PROBLEM FOR ONE-DIMENSIONAL SCHRODINGER EQUATION WITH AN ENERGY-DEPENDENT POTENTIAL .1.
JAULENT, M
JEAN, C
[J]. ANNALES DE L INSTITUT HENRI POINCARE SECTION A PHYSIQUE THEORIQUE, 1976, 25 (02): : 105 - 118
[10] THE ONE-DIMENSIONAL INVERSE SCATTERING PROBLEM FOR THE WAVE-EQUATION
GRINBERG, NI
[J]. MATHEMATICS OF THE USSR-SBORNIK, 1991, 70 (02): : 557 - 572

← 1 2 3 4 5 →