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The Riccati System and a Diffusion-Type Equation

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We discuss a method of constructing solutions of the initial value problem for diffusion-type equations in terms of solutions of certain Riccati and Ermakov-type systems. A nonautonomous Burgers-type equation is

We discuss a method of constructing solutions of the initial value problem for diffusion-type equations in terms of solutions of certain Riccati and Ermakov-type systems. A nonautonomous Burgers-type equation is also considered. Examples include, but are not limited to the Fokker-Planck equation in physics, the Black-Scholes equation and the Hull-White model in finance.

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Date Created
  • 2014-05-15

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Spiral laser beams in inhomogeneous media

Description

Explicit solutions of the inhomogeneous paraxial wave equation in a linear and quadratic approximation are applied to wave fields with invariant features, such as oscillating laser beams in a parabolic

Explicit solutions of the inhomogeneous paraxial wave equation in a linear and quadratic approximation are applied to wave fields with invariant features, such as oscillating laser beams in a parabolic waveguide and spiral light beams in varying media. A similar effect of superfocusing of particle beams in a thin monocrystal film, harmonic oscillations of cold trapped atoms, and motion in magnetic field are also mentioned.

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Date Created
  • 2013-08-15