an:03979612
Zbl 0606.35041
Gutkin, Eugene
Propagation of chaos and the Hopf-Cole transformation
EN
Adv. Appl. Math. 6, 413-421 (1985).
00150560
1985
j
35K55 35A30 37D45 35Q99
propagation of chaos; linearizing transformation; Hopf-Cole transformation; nonlinear evolution equations; contraction; N-body linear problems; approximate approach
In a previous paper it has been shown that Burgers' equation constitutes a limit of a contracted N-body problem when N tends to infinity. By proving that the L-operator may be transformed into a Laplacian \(\Delta\), by using an intertwining operator Q, an unsuccesful attempt was made to obtain a linearizing transformation for the Burgers equation in order to achieve a Hopf-Cole transformation.
In this paper the difficulties encountered previously were by-passed and a transformation closely related to the Hopf-Cole transformation was established. The transformation may be used to define the nonlinear evolution equations, which can be obtained by contraction from N-body linear problems, and distinguish the nonlinear equations which can be linearized by using the approximate approach established in this paper.
P.Theocaris