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Journal of Statistical Physics

, Volume 124, Issue 1, pp 191–205 | Cite as

Scaling Laws for the Multidimensional Burgers Equation with Quadratic External Potential

  • N. N. Leonenko
  • M. D. Ruiz-Medina
Article

Abstract

The reordering of the multidimensional exponential quadratic operator in coordinate-momentum space (see X. Wang, C.H. Oh and L.C. Kwek (1998). J. Phys. A.: Math. Gen. 31:4329–4336) is applied to derive an explicit formulation of the solution to the multidimensional heat equation with quadratic external potential and random initial conditions. The solution to the multidimensional Burgers equation with quadratic external potential under Gaussian strongly dependent scenarios is also obtained via the Hopf-Cole transformation. The limiting distributions of scaling solutions to the multidimensional heat and Burgers equations with quadratic external potential are then obtained under such scenarios.

Keywords

nonhomogeneous multidimensional Burgers equation quadratic external potential scaling laws spatiotemporal random fields strongly dependent random initial conditions 

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Copyright information

© Springer Science + Business Media, Inc. 2006

Authors and Affiliations

  • N. N. Leonenko
    • 1
  • M. D. Ruiz-Medina
    • 2
  1. 1.Cardiff School of MathematicsCardiff UniversityCardiffUnited Kingdom
  2. 2.Department of Statistics and Operations ResearchUniversity of GranadaGranadaSpain

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