2017/10/30 by Huijuan Zhou, Zhou, Huijuan, Chuanzhong Li +1
Physics and Astronomy · #Advanced Fiber Laser Technologies #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #Optics (physics.optics)
paper · pdf · doi:10.48550/arxiv.1710.10986
openalex publication_date 2017/10/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, by considering the potential application in two mode nonlinear waves in nonlinear fibers under a certain case, we define a coupled nonlinear Schrödinger equation(called Frobenius NLS equation) including its Lax pair. Afterwards, we construct the Darboux transformations of the Frobenius NLS equation. New solutions can be obtained from known seed solutions by the Dardoux transformations. Soliton solutions are generated from trivial seed solutions. Also we derive breather solutions q,r of the Frobenius NLS equation obtained from periodic seed solutions. Interesting enough, we find the amplitudes of r vary in size in different areas with period-like fluctuations in the background. This is very different from the solution q of the single-component classical nonlinear Schrödinger equation. Then, the rogue waves of the Frobenius NLS equation are given explicitly by a Taylor series expansion about the breather solutions q,r. Also the graph of rogue wave solution r shows that the rogue wave has fluctuations around the peak. The reason of this phenomenon should be in the dynamical dependence of r on q which is independent on r.