THE COLE-HOPF AND MIURA TRANSFORMATIONS REVISITED

Fritz Gesztesy, Helge Holden

Type: Book-Chapter

Publication Date: 2000-11-01

Citations: 10

DOI: https://doi.org/10.1142/9789812792167_0016

Abstract

Mathematical Physics and Stochastic Analysis, pp. 198-214 (2000) No AccessTHE COLE-HOPF AND MIURA TRANSFORMATIONS REVISITEDFRITZ GESZTESY and HELGE HOLDENFRITZ GESZTESYDepartment of Mathematics, University of Missouri, Columbia, MO 65211, USAhttp://www.math.missouri.edu/people/fgesztesy.html and HELGE HOLDENDepartment of Mathematical Sciences, Norwegian University of Science and Technology, N–7491 Trondheim, Norwayhttp://www.math.ntnu.no/~holden/https://doi.org/10.1142/9789812792167_0016Cited by:4 PreviousNext AboutSectionsPDF/EPUB ToolsAdd to favoritesDownload CitationsTrack CitationsRecommend to Library ShareShare onFacebookTwitterLinked InRedditEmail Abstract: An elementary yet remarkable similarity between the Cole-Hopf transformation relating the Burgers and heat equation and Miura's transformation connecting the KdV and mKdV equations is studied in detail. In the special (1 + 1)-dimensional case, our considerations apply to the entire hierarchy of Burgers evolution equations. Dedication: Dedicated with great pleasure to Ludwig Streit on the occasion of his 60th birthday. FiguresReferencesRelatedDetailsCited By 4Analogue of the Cole-Hopf transform for the incompressible Navier–Stokes equations and its applicationKoji Ohkitani1 March 2017 | Journal of Turbulence, Vol. 18, No. 5Bäcklund transformationsV. V. Zharinov6 January 2017 | Theoretical and Mathematical Physics, Vol. 189, No. 3О преобразовании БеклундаВиктор Викторович Жаринов and Victor Victorovich Zharinov1 Jan 2016 | Теоретическая и математическая физика, Vol. 189, No. 3Numerical study on comparison of Navier-Stokes and Burgers equationsKoji Ohkitani and Mark Dowker30 May 2012 | Physics of Fluids, Vol. 24, No. 5 Mathematical Physics and Stochastic AnalysisMetrics History PDF download

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+ PDF Chat	The stochastic Wick-type Burgers equation	1995	Helge Holden Tom Lindstrøm Bernt Øksendal Jan Ubøe Tusheng Zhang
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