TY - JOUR

T1 - Vector breathers in the Manakov system

AU - Gelash, Andrey

AU - Raskovalov, Anton

N1 - The main part of the work was supported by the Russian Science Foundation (grant no. 19-72-30028). The work of A.G. on Section 6 and Appendix Section A.2 was supported by RFBR grant no. 19-31-60028. The work of A.R. on Appendix Sections A.1 and A.4 was performed in the framework of the state assignment of the Russian Ministry of Science and Education “Quantum” No. AAAA-A18-118020190095-4. The authors thank participants of Prof. V.E. Zakharov's seminar “Nonlinear Waves” and, especially, Prof. E.A. Kuznetsov for fruitful discussions.

PY - 2023/4/1

Y1 - 2023/4/1

N2 - We study theoretically the nonlinear interactions of vector breathers propagating on an unstable wavefield background. As a model, we use the two-component extension of the one-dimensional focusing nonlinear Schrödinger equation—the Manakov system. With the dressing method, we generate the multibreather solutions to the Manakov model. As shown previously in [D. Kraus, G. Biondini, and G. Kovačič, Nonlinearity 28(9), 3101, (2015)], the class of vector breathers is presented by three fundamental types I, II, and III. Their interactions produce a broad family of the two-component (polarized) nonlinear wave patterns. First, we demonstrate that the type I and the types II and III correspond to two different branches of the dispersion law of the Manakov system in the presence of the unstable background. Then, we investigate the key interaction scenarios, including collisions of standing and moving breathers and resonance breather transformations. Analysis of the two-breather solution allows us to derive general formulas describing phase and space shifts acquired by breathers in mutual collisions. The found expressions enable us to describe the asymptotic states of the breather interactions and interpret the resonance fusion and decay of breathers as a limiting case of infinite space shift in the case of merging breather eigenvalues. Finally, we demonstrate that only type I breathers participate in the development of modulation instability from small-amplitude perturbations withing the superregular scenario, while the breathers of types II and III, belonging to the stable branch of the dispersion law, are not involved in this process. © 2023 Wiley Periodicals LLC.

AB - We study theoretically the nonlinear interactions of vector breathers propagating on an unstable wavefield background. As a model, we use the two-component extension of the one-dimensional focusing nonlinear Schrödinger equation—the Manakov system. With the dressing method, we generate the multibreather solutions to the Manakov model. As shown previously in [D. Kraus, G. Biondini, and G. Kovačič, Nonlinearity 28(9), 3101, (2015)], the class of vector breathers is presented by three fundamental types I, II, and III. Their interactions produce a broad family of the two-component (polarized) nonlinear wave patterns. First, we demonstrate that the type I and the types II and III correspond to two different branches of the dispersion law of the Manakov system in the presence of the unstable background. Then, we investigate the key interaction scenarios, including collisions of standing and moving breathers and resonance breather transformations. Analysis of the two-breather solution allows us to derive general formulas describing phase and space shifts acquired by breathers in mutual collisions. The found expressions enable us to describe the asymptotic states of the breather interactions and interpret the resonance fusion and decay of breathers as a limiting case of infinite space shift in the case of merging breather eigenvalues. Finally, we demonstrate that only type I breathers participate in the development of modulation instability from small-amplitude perturbations withing the superregular scenario, while the breathers of types II and III, belonging to the stable branch of the dispersion law, are not involved in this process. © 2023 Wiley Periodicals LLC.

UR - http://www.scopus.com/inward/record.url?partnerID=8YFLogxK&scp=85147036900

UR - https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcAuth=tsmetrics&SrcApp=tsm_test&DestApp=WOS_CPL&DestLinkType=FullRecord&KeyUT=000916440600001

U2 - 10.1111/sapm.12558

DO - 10.1111/sapm.12558

M3 - Article

VL - 150

SP - 841

EP - 882

JO - Studies in Applied Mathematics

JF - Studies in Applied Mathematics

SN - 0022-2526

IS - 3

ER -