Volume 129, Number 6, March 2020
|Number of page(s)||7|
|Section||Electromagnetism, Optics, Acoustics, Heat Transfer, Classical Mechanics, and Fluid Dynamics|
|Published online||27 April 2020|
Dispersionless evolution of inviscid nonlinear pulses
1 Université Paris-Saclay, CNRS, LPTMS - 91405 Orsay, France
2 Institute of Spectroscopy, Russian Academy of Sciences - Troitsk, Moscow, 108840, Russia
3 Moscow Institute of Physics and Technology - Institutsky lane 9, Dolgoprudny, Moscow region, 141701, Russia
Received: 8 December 2019
Accepted: 13 April 2020
We consider the one-dimensional dynamics of nonlinear non-dispersive waves. The problem can be mapped onto a linear one by means of the hodograph transform. We propose an approximate scheme for solving the corresponding Euler-Poisson equation which is valid for any kind of nonlinearity. The approach is exact for monoatomic classical gas and agrees very well with exact results and numerical simulations for other systems. We also provide a simple and accurate determination of the wave breaking time for typical initial conditions.
PACS: 47.40.-x – Compressible flows; shock waves / 42.65.Sf – Dynamics of nonlinear optical systems; optical instabilities, optical chaos and complexity, and optical spatio-temporal dynamics / 02.30.Jr – Partial differential equations
© EPLA, 2020
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