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Flavor oscillations can occur on very short spatial and temporal scales inthe dense neutrino media in a core-collapse supernova (CCSN) or binary neutronstar merger (BNSM) event. Although the dispersion relations (DRs) of the fastneutrino oscillations can be obtained by linearizing the equations of motion(EoM) before the emergence of any significant flavor conversion, one largelydepends on numerical calculations to understand this interesting phenomenon inthe nonlinear regime. In this work we demonstrate that there exist nontrivialsolutions to the flavor EoM that govern the fast oscillations inone-dimensional axisymmetric neutrino gases. These solutions represent acoherent flavor isospin wave similar to the magnetic spin wave in a lattice ofmagnetic dipoles. We also compute the DRs of such waves in some example caseswhich are closely related to the DRs of the fast neutrino oscillations obtainedin the linear regime. This result sheds new light on the long-term behavior offast neutrino oscillations which can have various implications for the CCSN andBNSM events.

Flavor isospin waves in one-dimensional axisymmetric neutrino gases