Gutkin, Eugene Propagation of chaos and the Hopf-Cole transformation. (English) Zbl 0606.35041 Adv. Appl. Math. 6, 413-421 (1985). 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. Reviewer: P.Theocaris Cited in 2 Documents MSC: 35K55 Nonlinear parabolic equations 35A30 Geometric theory, characteristics, transformations in context of PDEs 37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior 35Q99 Partial differential equations of mathematical physics and other areas of application Keywords:propagation of chaos; linearizing transformation; Hopf-Cole transformation; nonlinear evolution equations; contraction; N-body linear problems; approximate approach PDF BibTeX XML Cite \textit{E. Gutkin}, Adv. Appl. Math. 6, 413--421 (1985; Zbl 0606.35041) Full Text: DOI References: [1] Cole, J.D, On a quasilinear parabolic equation occurring in aerodynamics, Quart. appl. math., 9, 225-236, (1951) · Zbl 0043.09902 [2] Gutkin, E; Kac, M, Propagation of chaos and the Burgers equation, SIAM J. appl. math., 43, 971-980, (1983) · Zbl 0554.35104 [3] Hopf, E, The partial differential equation ut + uux = μuxx, Comm. pure appl. math., 3, 201-230, (1950) [4] McKean, H.P, Propagation of chaos for a class of nonlinear parabolic equations, (), 177-194 [5] \scE. Gutkin, Quantum nonlinear Schrödinger equation. I. Intertwining operators, Ann. Inst. Henri Poincaré, to appear. · Zbl 0614.35086 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.