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The Swift–Hohenberg equation (named after Jack B. Swift and Pierre Hohenberg) is a partial differential equation noted for its pattern-forming behaviour. It takes the form where u = u(x, t) or u = u(x, y, t) is a scalar function defined on the line or the plane, r is a real bifurcation parameter, and N(u) is some smooth nonlinearity. The equation is named after the authors of the paper, where it was derived from the equations for thermal convection. The webpage of Michael Cross contains some numerical integrators which demonstrate the behaviour of several Swift–Hohenberg-like systems.

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  • Swift-Hohenberg-Gleichung (de)
  • Swift-Hohenbergvergelijking (nl)
  • Swift–Hohenberg equation (en)
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  • Die Swift-Hohenberg-Gleichung (nach den beiden US-amerikanischen Physikern Jack B. Swift und Pierre C. Hohenberg) ist eine mathematische Modellgleichung zur Untersuchung von Musterbildungsprozessen. Eine mathematisch vereinfachte Form dieser Gleichung beschreibt das Muster der Faltenbildung von Papillarleisten (Dermatoglyphen) an Fingern, also das Muster von Fingerabdrücken, sowie das Muster der Bildung von Rillen auf eintrocknenden Rosinen. (de)
  • The Swift–Hohenberg equation (named after Jack B. Swift and Pierre Hohenberg) is a partial differential equation noted for its pattern-forming behaviour. It takes the form where u = u(x, t) or u = u(x, y, t) is a scalar function defined on the line or the plane, r is a real bifurcation parameter, and N(u) is some smooth nonlinearity. The equation is named after the authors of the paper, where it was derived from the equations for thermal convection. The webpage of Michael Cross contains some numerical integrators which demonstrate the behaviour of several Swift–Hohenberg-like systems. (en)
  • De Swift-Hohenbergvergelijking is een niet-lineaire partiële differentiaalvergelijking met als algemene vorm Hierin is of een reële functie van plaats en tijd, de laplace-operator, een reële bifurcatieparameter en een niet-lineaire functie van . De "kanonieke" Swift-Hohenbergvergelijking heeft , en is genoemd naar en , die deze vergelijking in 1977 voorstelden. (nl)
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  • Die Swift-Hohenberg-Gleichung (nach den beiden US-amerikanischen Physikern Jack B. Swift und Pierre C. Hohenberg) ist eine mathematische Modellgleichung zur Untersuchung von Musterbildungsprozessen. Eine mathematisch vereinfachte Form dieser Gleichung beschreibt das Muster der Faltenbildung von Papillarleisten (Dermatoglyphen) an Fingern, also das Muster von Fingerabdrücken, sowie das Muster der Bildung von Rillen auf eintrocknenden Rosinen. (de)
  • The Swift–Hohenberg equation (named after Jack B. Swift and Pierre Hohenberg) is a partial differential equation noted for its pattern-forming behaviour. It takes the form where u = u(x, t) or u = u(x, y, t) is a scalar function defined on the line or the plane, r is a real bifurcation parameter, and N(u) is some smooth nonlinearity. The equation is named after the authors of the paper, where it was derived from the equations for thermal convection. The webpage of Michael Cross contains some numerical integrators which demonstrate the behaviour of several Swift–Hohenberg-like systems. (en)
  • De Swift-Hohenbergvergelijking is een niet-lineaire partiële differentiaalvergelijking met als algemene vorm Hierin is of een reële functie van plaats en tijd, de laplace-operator, een reële bifurcatieparameter en een niet-lineaire functie van . De "kanonieke" Swift-Hohenbergvergelijking heeft , en is genoemd naar en , die deze vergelijking in 1977 voorstelden. (nl)
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