6533b836fe1ef96bd12a0bf1
RESEARCH PRODUCT
Analytic solutions and Singularity formation for the Peakon b--Family equations
Giuseppe Maria CocliteVincenzo SciaccaFrancesco Garganosubject
PhysicsAbstract Cauchy-Kowalewski theoremApplied MathematicsNumerical analysisComplex singularitiesNumerical Analysis (math.NA)Spectral analysisFourier spectrumRate of decayPeakonAnalytic solutionMomentumSingularityMathematics - Analysis of PDEsb-family equationFOS: MathematicsSpectral analysis Complex singularities b-family equation Analytic solution Abstract Cauchy-Kowalewski theoremMathematics - Numerical AnalysisComplex planeSettore MAT/07 - Fisica MatematicaMathematical physicsSign (mathematics)Analysis of PDEs (math.AP)description
This paper deals with the well-posedness of the b-family equation in analytic function spaces. Using the Abstract Cauchy-Kowalewski theorem we prove that the b-family equation admits, locally in time, a unique analytic solution. Moreover, if the initial data is real analytic and it belongs to H s with s>3/2, and the momentum density u 0-u 0, xx does not change sign, we prove that the solution stays analytic globally in time, for b≥1. Using pseudospectral numerical methods, we study, also, the singularity formation for the b-family equations with the singularity tracking method. This method allows us to follow the process of the singularity formation in the complex plane as the singularity approaches the real axis, estimating the rate of decay of the Fourier spectrum.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2012-01-01 |