TY - JOUR

T1 - The toda rarefaction problem

AU - Deift, Percy

AU - Kamvissis, Spyridon

AU - Kriecherbauer, Thomas

AU - Zhou, Xin

PY - 1996/1

Y1 - 1996/1

N2 - 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 one-dimensional semi-infinite 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problem in which the driving particle now moves away from the lattice at fixed speed, in analogy with a piston being withdrawn, as it were, from a container filled with gas.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 Riemann-Hilbert factorization formulation of the related inverse scattering problem. In the case where the speed 2|a| 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 In other words, in analogy with a piston being withdrawn too rapidly from a container filled with gas, cavitation develops.

AB - 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 one-dimensional semi-infinite 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problem in which the driving particle now moves away from the lattice at fixed speed, in analogy with a piston being withdrawn, as it were, from a container filled with gas.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 Riemann-Hilbert factorization formulation of the related inverse scattering problem. In the case where the speed 2|a| 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 In other words, in analogy with a piston being withdrawn too rapidly from a container filled with gas, cavitation develops.

UR - http://www.scopus.com/inward/record.url?scp=0030539847&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0030539847&partnerID=8YFLogxK

U2 - 10.1002/(SICI)1097-0312(199601)49:1<35::AID-CPA2>3.0.CO;2-8

DO - 10.1002/(SICI)1097-0312(199601)49:1<35::AID-CPA2>3.0.CO;2-8

M3 - Article

AN - SCOPUS:0030539847

SN - 0010-3640

VL - 49

SP - 35

EP - 83

JO - Communications on Pure and Applied Mathematics

JF - Communications on Pure and Applied Mathematics

IS - 1

ER -