# Wiktor Eckhaus > Mediated Wiki article. Canonical URL: https://mediated.wiki/source/Wiktor_Eckhaus > Markdown URL: https://mediated.wiki/source/Wiktor_Eckhaus.md > Source: https://en.wikipedia.org/wiki/Wiktor_Eckhaus > Source revision: 1346362204 > License: Creative Commons Attribution-ShareAlike 4.0 International (https://creativecommons.org/licenses/by-sa/4.0/) {{Short description|Polish–Dutch mathematician (1930-2000)}} {{Infobox scientist | name = Wiktor Eckhaus | image = Wiktor Eckhaus.jpg | image_size = 150px | caption = | birth_date = {{birth date|1930|6|28|df=y}}See {{harvtxt|Eckhaus|1997}} and {{harvtxt|Doelman|Duistermaat|Grasman|van Harten|2001}} for a discussion on his date and place of birth. | birth_place = [Stanisławów](/source/Iwano-Frankiwsk), [Poland](/source/Poland) | death_date = {{death date and age|2000|10|1|1930|6|28|df=y}} | death_place = [Amstelveen](/source/Amstelveen),{{citation | url=http://www.dwc.knaw.nl/biografie/pmknaw/?pagetype=authorDetail&aId=PE00000082 |accessdate=2014-09-06 |publisher=[Koninklijke Nederlandse Akademie van Wetenschappen](/source/Royal_Netherlands_Academy_of_Arts_and_Sciences) |title=Wiktor Eckhaus (1929 – 2000)}} [Netherlands](/source/Netherlands) | field = [mathematics](/source/mathematics),
[aerodynamics](/source/aerodynamics) | work_institution = [Utrecht University](/source/Utrecht_University),
[Delft University of Technology](/source/Delft_University_of_Technology),
[National Aerospace Laboratory](/source/Royal_Netherlands_Aerospace_Centre) | alma_mater = [Massachusetts Institute of Technology](/source/Massachusetts_Institute_of_Technology) | doctoral_advisor = [Leon Trilling](/source/Leon_Trilling) | doctoral_students = [Arjen Doelman](/source/Arjen_Doelman) | known_for = [Eckhaus instability](/source/Eckhaus_instability)
[Eckhaus equation](/source/Eckhaus_equation) | prizes = | religion = | footnotes = }} '''Wiktor Eckhaus''' (28 June 1930 – 1 October 2000) was a Polish–Dutch [mathematician](/source/mathematician), known for his work on the field of [differential equations](/source/differential_equations). He was Professor Emeritus of Applied Mathematics at the [Utrecht University](/source/Utrecht_University). ==Biography== Eckhaus was born into a wealthy family, and raised in [Warsaw](/source/Warsaw) where his father was managing a fur company. During the German occupation of Poland, he, his mother and sister had to hide because of their Jewish descent. His father, after being a prisoner of war, joined the Russian Army. After the war, in 1947, the re-united family came to [Amsterdam](/source/Amsterdam) – via a refugee camp in Austria. Wiktor passed the state exam of the [Hogere Burgerschool](/source/Hogere_Burgerschool) in 1948, and started to study [aeronautics](/source/aeronautics) at the [Delft University of Technology](/source/Delft_University_of_Technology). Following his graduation he worked with the [National Aerospace Laboratory](/source/Royal_Netherlands_Aerospace_Centre) in Amsterdam, from 1953 till 1957. In the period 1957–1960 he worked at the [Massachusetts Institute of Technology](/source/Massachusetts_Institute_of_Technology), where Eckhaus earned a PhD in 1959 under [Leon Trilling](/source/Leon_Trilling) on a dissertation entitled ''"Some problems of unsteady flow with discontinuities"''. In 1960, he became a "maître de recherches" (senior research fellow) at the Department of Mechanics of the [Sorbonne](/source/University_of_Paris). In 1964 he was a visiting professor at the [University of Amsterdam](/source/University_of_Amsterdam) and the [Mathematical Centre](/source/Mathematical_Centre). Thereafter, in 1965, he became professor at the Delft University of Technology, in pure and applied mathematics and mechanics. From 1972 until his retirement in 1994, Eckhaus was professor of applied mathematics at the Utrecht University. Initially he studied the [flow](/source/fluid_flow) around [airfoil](/source/airfoil)s, leading to his research on the [stability](/source/hydrodynamic_stability) of solutions to (weakly) [nonlinear differential equation](/source/nonlinear_differential_equation)s. This resulted in what is now known as the ''Eckhaus instability criterion'' and ''Eckhaus instability'', appearing for instance as a secondary instability in models of [Rayleigh–Bénard convection](/source/Rayleigh%E2%80%93B%C3%A9nard_convection). Later, Eckhaus worked on [singular perturbation theory](/source/singular_perturbation_theory) and [soliton](/source/soliton) equations. In 1983 he treated strongly singular [relaxation oscillation](/source/relaxation_oscillation)s – called ''"canards"'' (French for ''"ducks"'') – resulting in his most-read paper ''"Relaxation oscillations including a standard chase on French ducks"''.{{harvtxt|Eckhaus|1983}} Eckhaus used standard methods of [analysis](/source/analysis), on a problem qualified before, by [Marc Diener](/source/Marc_Diener), as an example of a problem only treatable through the use of [non-standard analysis](/source/non-standard_analysis).{{scholarpedia |urlname=Canards |title=Canards |curator=Martin Wechselberger }} He became a member of the [Royal Netherlands Academy of Arts and Sciences](/source/Royal_Netherlands_Academy_of_Arts_and_Sciences) in 1987. ==Publications== {{refbegin}} * {{citation |first=W. |last=Eckhaus |title=Studies in nonlinear stability theory |publisher=Springer |series=Springer Tracts in Natural Philosophy |volume=6 |year=1965 |isbn= 978-3-642-88319-4 }} * {{citation |first=W. |last=Eckhaus |author-mask=2 |title=Matched asymptotic expansions and singular perturbations |publisher=North Holland |year=1973 |series=Mathematics Studies |volume=6 |isbn=978-0-7204-2600-7 }} * {{citation |first=W. |last=Eckhaus |author-mask=2 |title=Asymptotic analysis of singular perturbations |publisher=North Holland |year=1979 |series=Studies in Mathematics and its Applications |volume=9 |isbn=978-0-444-85306-6 }} * {{citation |first1=W. |last1=Eckhaus |author-mask=2 |first2=A. |last2=van Harten |title=The inverse scattering transformation and the theory of solitons – An introduction |publisher=North Holland |year=1981 |series=Mathematics Studies |volume=50 |isbn=978-0-444-55731-5 }} * {{citation |first=W. |last=Eckhaus |author-mask=2 |title=New approach to the asymptotic theory of nonlinear oscillations and wave propagation |journal=Journal of Mathematical Analysis and Applications |volume=49 |issue=3 |year=1975 |pages=575–611 |doi=10.1016/0022-247X(75)90200-0 |doi-access=free }} * {{citation |first=W. |last=Eckhaus |author-mask=2 |contribution=Relaxation oscillations including a standard chase on French ducks |title=Asymptotic Analysis II — |editor-first=F. |editor-last=Verhulst |series=Lecture Notes in Mathematics |volume=985 |publisher=Springer |year=1983 |isbn=978-3-540-12286-9 |doi=10.1007/BFb0062381 |pages=449–494 }} * {{citation |first=W. |last=Eckhaus |author-mask=2 |title=The Ginzburg–Landau manifold is an attractor |journal=Journal of Nonlinear Science |volume=3 |year=1993 |issue=1 |pages=329–348 |doi=10.1007/BF02429869 |bibcode=1993JNS.....3..329E |s2cid=122662589 }} * {{citation |first1=W. |last1=Eckhaus |author-mask=2 |first2=E.M. |last2=de Jager |title=Asymptotic solutions of singular perturbation problems for linear differential equations of elliptic type |journal=Arch. Rat. Mech. Anal. |volume=23 |issue=1 |year=1966 |pages=26–86 |doi=10.1007/BF00281135 |bibcode=1966ArRMA..23...26E |s2cid=843282 |url=https://research.utwente.nl/en/publications/91969077-6880-43af-956f-8bccba35bbea }} * {{citation |first=W. |last=Eckhaus |author-mask=2 |title=Witus en de jaren van angst – Een reconstructie |publisher=Bas Lubberhuizen |year=1997 |language=nl |trans-title= Witus and the years of fear – A reconstruction | isbn=9789073978690 | type=Autobiography }} {{refend}} ==Notes== {{reflist}} ==References== {{refbegin}} * {{citation | first1=A. |last1=Doelman |first2=H. |last2=Duistermaat |first3=J. |last3=Grasman |first4=A. |last4=van Harten |title=In memoriam Wiktor Eckhaus |language=nl |journal=Nieuw Archief voor Wiskunde | volume=2 |issue=1 |pages=18–20 |year=2001 |url=http://www.math.leidenuniv.nl/~doelman/HP_PUB/imWE.pdf |publisher=[Koninklijk Wiskundig Genootschap](/source/Royal_Dutch_Mathematical_Society) |postscript=. }}
Also appeared as: {{citation | first1=J.J. |last1=Duistermaat |first2=A. |last2=Doelman |first3=J. |last3=Grasman |first4=A. |last4=van Harten |title=Levensbericht W. Eckhaus |trans-title=Eulogy W. Eckhaus |language=nl |journal=Levensberichten en Herdenkingen |publisher=[Koninklijke Nederlandse Akademie van Wetenschappen](/source/Royal_Netherlands_Academy_of_Arts_and_Sciences) |year=2003 |location=Amsterdam |pages=19–24 |url=http://www.dwc.knaw.nl/DL/levensberichten/PE00000082.pdf |postscript=. }} {{refend}} ==External links== * {{MathGenealogy|id=49577}} {{Authority control}} {{DEFAULTSORT:Eckhaus, Wiktor}} Category:1930 births Category:2000 deaths Category:People from Ivano-Frankivsk Category:People from Stanisławów Voivodeship Category:Ukrainian Jews Category:Polish emigrants to the Netherlands Category:Dutch people of Ukrainian-Jewish descent Category:Aerodynamicists Category:20th-century Dutch mathematicians Category:MIT School of Engineering alumni Category:Academic staff of Utrecht University Category:Academic staff of the Delft University of Technology Category:Members of the Royal Netherlands Academy of Arts and Sciences --- Adapted from the Wikipedia article [Wiktor Eckhaus](https://en.wikipedia.org/wiki/Wiktor_Eckhaus) by Wikipedia contributors ([contributor history](https://en.wikipedia.org/wiki/Wiktor_Eckhaus?action=history)). Available under [Creative Commons Attribution-ShareAlike 4.0 International](https://creativecommons.org/licenses/by-sa/4.0/). Changes may have been made.