Physics Letters A 333 (2004) 334–340 www.elsevier.com/locate/pla Hypersonic flow past slender bodies in dispersive hydrodynamics G.A. El a,b,∗ , V.V. Khodorovskii c , A.V. Tyurina b a School of Mathematical and Information Sciences, Coventry University, Coventry, UK b Institute of Terrestrial Magnetism, Ionosphere and Radio Wave Propagation, Russian Academy of Sciences, Troitsk, Moscow Region, Russia c Information Science Department, St. Petersburg State University of Culture and Arts, St. Petersburg, Russia Received 9 October 2004; accepted 12 October 2004 Available online 27 October 2004 Communicated by V.M. Agranovich Abstract The problem of two-dimensional steady hypersonic flow past a slender body is formulated for dispersive media. It is shown that for the hypersonic flow, the original 2 + 0 boundary-value problem is asymptotically equivalent to the 1 + 1 piston problem for the fully nonlinear flow in the same physical system, which allows one to take advantage of the analytic methods developed for one-dimensional systems. This type of equivalence, well known in ideal Euler gas dynamics, has not been established for dispersive hydrodynamics so far. Two examples pertaining to collisionless plasma dynamics are considered.  2004 Elsevier B.V. All rights reserved. Keywords: Nonlinear flow past body; Dispersive shock; Hypersonic flow 1. Introduction The problem of supersonic flow around objects is one of the central problems in classical hydrody- namics [1,2]. The nonlinear system of Euler equa- tions describing established (time-independent) two- dimensional supersonic flows in ideal gas dynamics is hyperbolic. When the supersonic flow occurs around objects it is accompanied by the onset of singulari- * Corresponding author. E-mail address: g.el@coventry.ac.uk (G.A. El). ties of the wave breakdown type. In the vicinity of the breakdown point, the higher order corrections in the equations of ideal gas dynamics should be taken into account. In ordinary hydrodynamics, when these terms are dissipative, this gives rise to an oblique compression jump (an analog of a shock in the one- dimensional nonstationary case). In dispersive continuous media, where dissipa- tion is small enough or negligible, the resolution of a singularity happens through generation of small- scale nonlinear waves. What forms here instead of an oblique compression jump is a wedge shaped region of space occupied by small-scale nonlinear oscilla- 0375-9601/$ – see front matter  2004 Elsevier B.V. All rights reserved. doi:10.1016/j.physleta.2004.10.036