abelianabsadditivealgebraalgebrasanalysisapplicationsarisingautomatabacklundbaxtercellularclassicalclassificationclustercoefficientscombinatorialcomplexconnectionconservationcrystalcrystalscurvesdarbouxdeformationdeformationsdegreedifferencedifferentialdimensionaldisdiscretizationdynamicalellipticequationequationsextendedfactorsfieldsfiniteformfunctionfunctionsgaloisgeometricgeometrygrouphierarchyhirotahypergeometricidentitiesiiinitialintegrabilityintegralsinvariantskahankdvkimuralagrangianlatticelawslaxlielinearmanymapmappingsmapsmatricesmatrixmethodmodelmonodromymovingmultiscalenlsnonlinearorderoriginorthogonalpainlevepairspartialpentagramperiodicpoissonpolynomialpolynomialspreservingprincipleproblemspropertiesqrtquadquantumrecentrecurrencereductionreductionsresultssecondsequencesseriessolidsolitonsolitonssolutionssolvablespacespecialstructuresstudysurfacessymmetrysystemtheoremtheoriestheorytimetransformationstropicaltypeultradiscreteunificationvariablesvariationalviayang