Complex Blow-Up in Burgers' Equation: an Iterative Approach

1996/10/31 by Nalini Joshi, Joshi, Nalini, Johannes A. Petersen +1
Physics and Astronomy · #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #nlin.SI #solv-int

paper · pdf · doi:10.48550/arxiv.solv-int/9610013

11 pages in LaTeX. To appear in Bull. Aust. Math. Soc

arxiv created 1996/10/31 · arxiv updated 2009/11/30

Abstract

We show that for a given holomorphic noncharacteristic surface S in two-dimensional complex space, and a given holomorphic function on S, there exists a unique meromorphic solution of Burgers' equation which blows up on S. This proves the convergence of the formal Laurent series expansion found by the Painlevé test. The method used is an adaptation of Nirenberg's iterative proof of the abstract Cauchy-Kowalevski theorem.

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