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Nonlinear Dynamics

, Volume 95, Issue 3, pp 1767–1780 | Cite as

Energy-sharing collisions and the dynamics of degenerate solitons in the nonlocal Manakov system

  • S. Stalin
  • M. SenthilvelanEmail author
  • M. Lakshmanan
Original Paper

Abstract

In this paper, by considering the degenerate two bright soliton solution of the nonlocal Manakov system, we bring out three different types of energy-sharing collisions for two different parametric conditions. Among the three, two of them are new which do not exist in the local Manakov equation. By performing an asymptotic analysis to the degenerate two-soliton solution, we explain the changes which occur in the quasi-intensity/quasi-power, phase shift and relative separation distance during the collision process. Remarkably, the intensity redistribution reveals that in the new types of shape-changing collisions, the energy difference of soliton in the two modes is not preserved during collision. In contrast to this, in the other shape-changing collision, the total energy of soliton in the two modes is conserved during collision. In addition to this, by tuning the imaginary parts of the wave numbers, we observe localized resonant patterns in both the scenarios. We also demonstrate the existence of bound states in the nonlocal Manakov equation during the collision process for certain parametric values.

Keywords

Coupled nonlocal nonlinear Schrödinger equations Hirota’s bilinear method Soliton solutions 

Notes

Acknowledgements

The work of MS forms part of a research project sponsored by DST-SERB, Government of India, under the Grant No. EMR/2016/001818. The research work of ML is supported by a SERB Distinguished Fellowship and also forms part of the DAE-NBHM research project (2/48 (5)/2015/NBHM (R.P.)/R&D-II/14127).

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

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Copyright information

© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.Centre for Nonlinear Dynamics, School of PhysicsBharathidasan UniversityTiruchirappalliIndia

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