Search results for " Borel and power series methods"

showing 2 items of 2 documents

Complex singularities in KdV solutions

2016

In the small dispersion regime, the KdV solution exhibits rapid oscillations in its spatio-temporal dependence. We show that these oscillations are caused by the presence of complex singularities that approach the real axis. We give a numerical estimate of the asymptotic dynamics of the poles.

Complex singularities Padé approximation Borel and power series methods Dispersive shocksApplied MathematicsGeneral MathematicsNumerical analysis010102 general mathematicsMathematical analysis01 natural sciences010305 fluids & plasmasAsymptotic dynamics0103 physical sciencesPadé approximantGravitational singularity0101 mathematicsAlgebra over a fieldKorteweg–de Vries equationDispersion (water waves)Complex planeMathematics
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Complex singularities and PDEs

2015

In this paper we give a review on the computational methods used to capture and characterize the complex singularities developed by some relevant PDEs. We begin by reviewing the classical singularity tracking method and give an example of application using the Burgers equation as a case study. This method is based on the analysis of the Fourier spectrum of the solution and it allows to determine and characterize the complex singularity closest to the real domain. We then introduce other methods generally used to detect the hidden singularities. In particular we show some applications of the Padé approximation, of the Kida method, and of Borel-Polya method. We apply these techniques to the s…

Physics::Fluid DynamicsComplex singularity Fourier transforms Padé approximation Borel and power series methods dispersive shocks fluid mechanics zero viscosity.Fluid Dynamics (physics.flu-dyn)FOS: Physical sciencesMathematical Physics (math-ph)Physics - Fluid DynamicsMathematical Physics
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