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Scaling Laws for the Multidimensional Burgers Equation with Quadratic External Potential

Leonenko, Nikolai N. ORCID: and Ruiz-Medina, M. D. 2006. Scaling Laws for the Multidimensional Burgers Equation with Quadratic External Potential. Journal of Statistical Physics 124 (1) , pp. 191-205. 10.1007/s10955-006-9136-5

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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.

Item Type: Article
Date Type: Publication
Status: Published
Schools: Mathematics
Subjects: Q Science > QA Mathematics
Uncontrolled Keywords: nonhomogeneous multidimensional Burgers equation - quadratic external potential - scaling laws - spatiotemporal random fields - strongly dependent random initial conditions
Publisher: Springer
ISSN: 0022-4715
Last Modified: 20 Oct 2022 07:54

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