The N-wave equations with PT symmetry

被引：36

作者：

Gerdjikov, V. S. ^{[1
]}

Grahovski, G. G. ^{[1
,2
]}

Ivanov, R. I. ^{[3
]}

机构：

[1] Bulgarian Acad Sci, Inst Nucl Res & Nucl Energy, Sofia, Bulgaria

[2] Univ Essex, Dept Math Sci, Colchester, Essex, England

[3] Dublin Inst Technol, Sch Math Sci, Dublin, Ireland

来源：

THEORETICAL AND MATHEMATICAL PHYSICS | 2016年 / 188卷 / 03期

关键词：

integrable system; PT symmetry; inverse scattering transform; soliton solution; INVERSE SCATTERING TRANSFORM; BEALS-COIFMAN SYSTEM; SIMPLE LIE-ALGEBRAS; 3-WAVE INTERACTION; PSEUDO-HERMITICITY; PT-SYMMETRY; REDUCTIONS; SOLITONS; OPTICS;

D O I：

10.1134/S0040577916090038

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We study extensions of N-wave systems with PT symmetry and describe the types of (nonlocal) reductions leading to integrable equations invariant under the P (spatial reflection) and T (time reversal) symmetries. We derive the corresponding constraints on the fundamental analytic solutions and the scattering data. Based on examples of three-wave and four-wave systems (related to the respective algebras sl(3,C) and so(5,C)), we discuss the properties of different types of one- and two-soliton solutions. We show that the PT-symmetric three-wave equations can have regular multisoliton solutions for some specific choices of their parameters.

引用

页码：1305 / 1321

页数：17

共 50 条

[1] Solitons in PT-symmetric nonlinear lattices [J].

Abdullaev, Fatkhulla Kh. ;

Kartashov, Yaroslav V. ;

Konotop, Vladimir V. ;

Zezyulin, Dmitry A. .

PHYSICAL REVIEW A, 2011, 83 (04)

[2] Inverse scattering transform for the integrable nonlocal nonlinear Schrodinger equation [J].

Ablowitz, Mark J. ;

Musslimani, Ziad H. .

NONLINEARITY, 2016, 29 (03) :915-946

[3] Integrable discrete PT symmetric model [J].

Ablowitz, Mark J. ;

Musslimani, Ziad H. .

PHYSICAL REVIEW E, 2014, 90 (03)

[4] Integrable Nonlocal Nonlinear Schrodinger Equation [J].

Ablowitz, Mark J. ;

Musslimani, Ziad H. .

PHYSICAL REVIEW LETTERS, 2013, 110 (06)

[5] SOLITONS AND 4-WAVE-MIXING [J].

ACKERHALT, JR ;

MILONNI, PW .

PHYSICAL REVIEW A, 1986, 33 (05) :3185-3198

[6]

[Anonymous], 1980, Theory of Solitons. Inverse Problem Method

[7] Dimer with gain and loss: Integrability and PT-symmetry restoration [J].

Barashenkov, I. V. ;

Pelinovsky, D. E. ;

Dubard, P. .

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 2015, 48 (32)

[8] Hamiltonian formulation of the standard PT-symmetric nonlinear Schrodinger dimer [J].

Barashenkov, I. V. .

PHYSICAL REVIEW A, 2014, 90 (04)

[9] SCATTERING AND INVERSE SCATTERING FOR 1ST-ORDER SYSTEMS .2. [J].

BEALS, R ;

COIFMAN, RR .

INVERSE PROBLEMS, 1987, 3 (04) :577-593

[10] Making sense of non-Hermitian Hamiltonians [J].

Bender, Carl M. .

REPORTS ON PROGRESS IN PHYSICS, 2007, 70 (06) :947-1018

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