An asymptotic limit of a class of Cahn–Hilliard systems is investigated to obtain a general nonlinear diffusion equation. The target diffusion equation may reproduce a number of well-known model equations: Stefan problem, porous media equation, Hele-Shaw profile, nonlinear diffusion of singular logarithmic type, nonlinear diffusion of Penrose–Fife type, fast diffusion equation and so on. Namely...

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We introduce a new notion of “matrix potential” to nonlinear optical systems. In terms of a matrix potential g, we present a gauge field theoretic formulation of the Maxwell-Bloch equation that provides a semiclassical description of the propagation of optical pulses through resonant multi-level media. We show that the Bloch part of the equation can solved identically through g and the remainin...