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

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.