Trace formulas and continuous dependence of spectra for the periodic conservative Camassa–Holm flow Jonathan Eckhardt Aleksey Kostenko Noema Nicolussi 2134/11860755.v1 https://repository.lboro.ac.uk/articles/journal_contribution/Trace_formulas_and_continuous_dependence_of_spectra_for_the_periodic_conservative_Camassa_Holm_flow/11860755 <div>This article is concerned with the isospectral problem −f" +1/4f = z ωf + z<sup>2</sup>vf </div><div>for the periodic conservative Camassa–Holm flow, where ω is a periodic real distribution in H<sup>−1</sup> loc (R) and υ is a periodic non-negative Borel measure on . We develop basic Floquet theory for this problem, derive trace formulas for the associated spectra and establish continuous dependence of these spectra on the coefficients with respect to a weak⁎ topology.</div> 2020-02-18 14:12:20 Periodic Camassa-Holm flow Spectrum Trace formulas Continuous dependence Science & Technology Physical Sciences Mathematics ALGEBRO-GEOMETRIC SOLUTIONS SHALLOW-WATER EQUATION WEAK SOLUTIONS math.SP math.CA Primary 34L05, 34B07, Secondary 34L15, 37K15 General Mathematics Pure Mathematics Applied Mathematics