The N-wave equations with PT symmetry

V. S. Gerdjikov; G. G. Grahovski; R. I. Ivanov

doi:10.1134/S0040577916090038

The N-wave equations with PT symmetry

V. S. Gerdjikov, G. G. Grahovski, R. I. Ivanov

School of Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

Abstract

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.

Original language	English
Pages (from-to)	1305-1321
Number of pages	17
Journal	Theoretical and Mathematical Physics(Russian Federation)
Volume	188
Issue number	3
DOIs	https://doi.org/10.1134/S0040577916090038
Publication status	Published - 1 Sep 2016

Keywords

PT symmetry
integrable system
inverse scattering transform
soliton solution

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10.1134/S0040577916090038

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AU - Gerdjikov, V. S.

AU - Grahovski, G. G.

AU - Ivanov, R. I.

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Y1 - 2016/9/1

N2 - 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.

AB - 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.

KW - PT symmetry

KW - integrable system

KW - inverse scattering transform

KW - soliton solution

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DO - 10.1134/S0040577916090038

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EP - 1321

JO - Theoretical and Mathematical Physics(Russian Federation)

JF - Theoretical and Mathematical Physics(Russian Federation)

IS - 3

ER -

The N-wave equations with PT symmetry

Abstract

Keywords

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