L. -C. Zhao | Searcharxiv

arXiv2022

Dirac Monopoles in Rogue Waves

We for the first time demonstrate that the widely existed nonlinear waves such as rogue waves, contain Dirac monopoles. We find that the density zeros of these nonlinear waves on an extended complex plane can constitute the Dirac virtual magnetic monopole fields with a quantized flux of elementary $π$. We then can explain the exotic property of ``appearing from nowhere and disappearing without a trace" of rogue waves by means of a Dirac monopole collision mechanism. The maximum amplification ratio and multiple phase steps of high-order rogue waves are found to be closely related to the number of their contained monopoles. Important implications of the intrinsic virtual magnetic monopole fields are discussed.

nlin.PS↗

arXiv2022

Exact analytical soliton solutions of $N$-component coupled nonlinear Schrödinger equations with arbitrary nonlinear parameters

Exact analytical soliton solutions play an important role in soliton fields. Soliton solutions were obtained with some special constraints on the nonlinear parameters in nonlinear coupled systems, but they usually do not holds in real physical systems. We successfully release all usual constrain conditions on nonlinear parameters for exact analytical vector soliton solutions in $N$-component coupled nonlinear Schrödinger equations. The exact soliton solutions and their existence condition are given explicitly. Applications of these results are discussed in several present experimental parameters regimes. The results would motivate experiments to observe more novel vector solitons in nonlinear optical fibers, Bose-Einstein condensates, and other nonlinear coupled systems.

nlin.PS↗