Math @ Duke

Publications [#244265] of Xin Zhou
Papers Published
 Deift, P; Kamvissis, S; Kriecherbauer, T; Zhou, X, The toda rarefaction problem,
Communications on Pure and Applied Mathematics, vol. 49 no. 1
(1996),
pp. 3583 [MR97e:34023]
(last updated on 2017/12/17)
Abstract: In the Toda shock problem (see [7], [11], [8], and also [3]) one considers a driving particle moving with a fixed velocity 2a and impinging on a onedimensional semiinfinite lattice of particles, initially equally spaced and at rest, and interacting with exponential forces. In this paper we consider the related Toda rarefaction problem in which the driving particle now moves away from the lattice at fixed speed, in analogy with a piston being withdrawn, as it were, from a container filled with gas. We make use of the RiemannHilbert factorization formulation of the related inverse scattering problem. In the case where the speed 2a of the driving particle is sufficiently large (a > 1), we show that the particle escapes from the lattice, which then executes a free motion of the type studied, for example, in [5]. In other words, in analogy with a piston being withdrawn too rapidly from a container filled with gas, cavitation develops. © 1996 John Wiley & Sons, Inc.


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