Finite Gap Conditions and Small Dispersion Asymptotics for the Classical Periodic Benjamin-Ono Equation

@article{Moll2019FiniteGC,
  title={Finite Gap Conditions and Small Dispersion Asymptotics for the Classical Periodic Benjamin-Ono Equation},
  author={A. Moll},
  journal={arXiv: Mathematical Physics},
  year={2019}
}
  • A. Moll
  • Published 2019
  • Mathematics, Physics
  • arXiv: Mathematical Physics
  • For any smooth spatially-periodic solution of the Benjamin-Ono equation, the work of Nazarov-Sklyanin determines a dispersive action profile, a piecewise-linear function of an auxiliary real variable whose values are all conserved by the flow. In this paper, we derive three results for dispersive action profiles (finite gap conditions, convex action profiles in the small dispersion limit, and frozen regions) and relate each to the dispersive dynamics (the Satsuma-Ishimori multi-phase solutions… CONTINUE READING

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