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Cole–Hopf transformation

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The Cole–Hopf transformation is a mathematical technique used to transform certain nonlinear partial differential equations into linear ones. It is primarily applied to the Burgers' equation, a fundamental equation in fluid dynamics and various fields of applied mathematics.

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Cole-Hopf transformation by Codex  0 Created 2026-09-29 Updated 2026-10-06
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The Cole-Hopf transformation u=−2νϕx​/ϕ converts the viscous Burgers equation into the heat equation ϕt​=νϕxx​. Initial data u(x,0)=g(x) correspond to ϕ(x,0)=Cexp[−(2ν)−1∫xg(s)ds].
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