Rogue waves in the nonlocal PT-symmetric nonlinear Schrödinger equation

Rogue waves in the nonlocal PT -symmetric nonlinear Schrödinger (NLS) equation are studied by Darboux transformation. Three types of rogue waves are derived, and their explicit expressions in terms of Schur polynomials are presented. These rogue waves show a much wider variety than those in the loca...

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Bibliographic Details
Published inLetters in mathematical physics Vol. 109; no. 4; pp. 945 - 973
Main Authors Yang, Bo, Yang, Jianke
Format Journal Article
LanguageEnglish
Published Dordrecht Springer Netherlands 03.04.2019
Springer Nature B.V
Subjects
Complex Systems
Geometry
Group Theory and Generalizations
Mathematical and Computational Physics
Physics
Physics and Astronomy
Polynomials
Schrodinger equation
Singularities
Theoretical
Schur polynomials
37K35
Rogue waves
Nonlocal NLS equation
35Q55
35C08
Darboux transformation
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Summary:Rogue waves in the nonlocal PT -symmetric nonlinear Schrödinger (NLS) equation are studied by Darboux transformation. Three types of rogue waves are derived, and their explicit expressions in terms of Schur polynomials are presented. These rogue waves show a much wider variety than those in the local NLS equation. For instance, the polynomial degrees of their denominators can be not only n ( n + 1 ) , but also n ( n - 1 ) + 1 and n 2 , where n is an arbitrary positive integer. Dynamics of these rogue waves is also examined. It is shown that these rogue waves can be bounded for all space and time or develop collapsing singularities, depending on their types as well as values of their free parameters. In addition, the solution dynamics exhibits rich patterns, most of which have no counterparts in the local NLS equation.
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ISSN:0377-9017
1573-0530
DOI:10.1007/s11005-018-1133-5