Extended resolvent and inverse scattering with an application to KPI

被引：11

作者：

Boiti, M ^{[1
]}

Pempinelli, F

Pogrebkov, AK

Prinari, B

机构：

[1] Univ Lecce, Dipartimento Fis, I-73100 Lecce, Italy

[2] Sez INFN, I-73100 Lecce, Italy

[3] VA Steklov Math Inst, Moscow, Russia

来源：

JOURNAL OF MATHEMATICAL PHYSICS | 2003年 / 44卷 / 08期

关键词：

D O I：

10.1063/1.1587874

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We present in detail an extended resolvent approach for investigating linear problems associated to 2+1 dimensional integrable equations. Our presentation is based as an example on the nonstationary Schrodinger equation with potential being a perturbation of the one-soliton potential by means of a decaying two-dimensional function. Modification of the inverse scattering theory as well as properties of the Jost solutions and spectral data as follows from the resolvent approach are given. (C) 2003 American Institute of Physics.

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页码：3309 / 3340

页数：32

相关论文

共 17 条

[1] PROPERTIES OF SOLUTIONS OF THE KADOMTSEV-PETVIASHVILI-I EQUATION [J].

BOITI, M ;

PEMPINELLI, F ;

POGREBKOV, A .

JOURNAL OF MATHEMATICAL PHYSICS, 1994, 35 (09) :4683-4718

[2] RESOLVENT APPROACH FOR THE NONSTATIONARY SCHRODINGER-EQUATION [J].

BOITI, M ;

PEMPINELLI, F ;

POGREBKOV, AK ;

POLIVANOV, MC .

INVERSE PROBLEMS, 1992, 8 (03) :331-364

[3] SPECTRAL TRANSFORM AND ORTHOGONALITY RELATIONS FOR THE KADOMTSEV-PETVIASHVILI-I EQUATION [J].

BOITI, M ;

LEON, JJP ;

PEMPINELLI, F .

PHYSICS LETTERS A, 1989, 141 (3-4) :96-100

[4] SOLUTIONS OF THE KPI EQUATION WITH SMOOTH INITIAL DATA [J].

BOITI, M ;

PEMPINELLI, F ;

POGREBKOV, A .

INVERSE PROBLEMS, 1994, 10 (03) :505-519

[5] Solving the Kadomtsev-Petviashvili equation with initial data not vanishing at large distances [J].

Boiti, M ;

Pempinelli, F ;

Pogrebkov, A .

INVERSE PROBLEMS, 1997, 13 (03) :L7-L10

[6] Towards an inverse scattering theory for two-dimensional nondecaying potentials [J].

Boiti, M ;

Pempinelli, F ;

Pogrebkov, AK ;

Prinari, B .

THEORETICAL AND MATHEMATICAL PHYSICS, 1998, 116 (01) :741-781

[7] SOME NEW METHODS AND RESULTS IN THE THEORY OF (2+1)-DIMENSIONAL INTEGRABLE EQUATIONS [J].

BOITI, M ;

PEMPINELLI, F ;

POGREBKOV, AK .

THEORETICAL AND MATHEMATICAL PHYSICS, 1994, 99 (02) :511-522

[8] RESOLVENT APPROACH FOR 2-DIMENSIONAL SCATTERING PROBLEMS - APPLICATION TO THE NONSTATIONARY SCHRODINGER-PROBLEM AND THE KPI EQUATION [J].

BOITI, M ;

PEMPINELLI, F ;

POGREBKOV, AK ;

POLIVANOV, MC .

THEORETICAL AND MATHEMATICAL PHYSICS, 1992, 93 (02) :1200-1224

[9]

BOITI M, 1996, NONLINEAR PHYSICS TH, P37

[10]

DRYUMA V, 1974, SOV PHYS JETP, V19, P381