期刊
PHYSICAL REVIEW E
卷 93, 期 2, 页码 -出版社
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevE.93.020101
关键词
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资金
- EPSRC [EP/J019526/1]
- Engineering and Physical Sciences Research Council [EP/J019526/1] Funding Source: researchfish
- EPSRC [EP/J019526/1] Funding Source: UKRI
We derive the single integrodifferential wave equation for the probability density function of the position of a classical one-dimensional Levy walk with continuous sample paths. This equation involves a classical wave operator together with memory integrals describing the spatiotemporal coupling of the Levy walk. It is valid at all times, not only in the long time limit, and it does not involve any large-scale approximations. It generalizes the well-known telegraph or Cattaneo equation for the persistent random walk with the exponential switching time distribution. Several non-Markovian cases are considered when the particle's velocity alternates at the gamma and power-law distributed random times. In the strong anomalous case we obtain the asymptotic solution to the integrodifferential wave equation. We implement the nonlinear reaction term of Kolmogorov-Petrovsky-Piskounov type into our equation and develop the theory of wave propagation in reaction-transport systems involving Levy diffusion.
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