2014/12/20 by N. Vishnu Priya, M. Senthilvelan, Priya, N. Vishnu +1
Mathematics · Physics and Astronomy · #Advanced Fiber Laser Technologies #Breather #Connection (principal bundle) #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Instability #Mathematical analysis #Mathematics #Mixing (physics) #Modulation (music) #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #Nonlinear system #Pattern Formation and Solitons (nlin.PS) #Physics #Quantum mechanics #Rogue wave #Transformation (genetics) #nlin.PS #nlin.SI
paper · pdf · doi:10.48550/arxiv.1412.6647
14 pages, 3 figures, To appear in Wave Motion
arxiv created 2014/12/20 · openalex publication_date 2014/12/20 · arxiv updated 2014/12/23 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
We construct Darboux transformation of a coupled generalized nonlinear Schrödinger (CGNLS) equations and obtain exact analytic expressions of breather and rogue wave solutions. We also formulate the conditions for isolating these solutions. We show that the rogue wave solution can be found only when the four wave mixing parameter becomes real. We also investigate the modulation instability of the steady state solution of CGNLS system and demonstrate that it can occur only when the four wave mixing parameter becomes real. Our results give an evidence for the connection between the occurrence of rogue wave solution and the modulation instability.