A chemical response theory of the Toda lattice in an external mechanical perturbation

Zene Horii

Physica A: Statistical Mechanics and its Applications, 2004, vol. 337, issue 3, 398-410

Abstract: In the preceding paper, using the so-called flow variable representation, we reported the formulation of the Korteweg-deVries (KdV) and the Burgers equations to express mass transports. The transport theories were constructed by pertaining to correspondence with the Toda lattices. Our present purpose is to understand a connection between these nonlinear wave equations formulated independently from the generalized form of the Kawasaki–Ohta equation. For this purpose, we formulate the Burgers equation from the KdV in correspondence to a transition from the dispersive Toda lattice to a dissipative model. For this formulation, we employ an external mechanical perturbation method. The paper is concerned with a variation method as to how to prepare a perturbation Lax bracket for the Burgers formulation. Variations in one of the Lax operators are assumed to be ∂−1 as an obstruction operator against the convection flows expressed by ∂ in the repulsive potential field. We conclude that the obstruction is caused by attractive interactions. The main point is that the Burgers equation is transformed to a nonlinear diffusion equation by the Hopf–Cole transform. The variation method and the argumentation for the Burgers formulation are proved by this transformation.

Keywords: Lax bracket; External mechanical perturbation; Phase transition; Diffusion coefficient; Information-contraction; KdV eq. and Burgers eq. (search for similar items in EconPapers)
Date: 2004
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:337:y:2004:i:3:p:398-410

DOI: 10.1016/j.physa.2004.01.058

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