Dispersionless evolution of inviscid nonlinear pulses

Abstract

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.

References in corpus (6)

• Effective wave-equations for the dynamics of cigar-shaped and disc-shaped Bose condensates
• Measurements of Relative Phase in Binary Mixtures of Bose-Einstein Condensates
• Quasi-1D Bose-Einstein condensates in the dimensional crossover regime
• Dynamics of Bose-Einstein condensates in cigar-shaped traps
• Wave breaking and formation of dispersive shock waves in a defocusing nonlinear optical material
• Collision of rarefaction waves in Bose-Einstein condensates

Cited by in corpus (5)

• Quantitative Analysis of Shock Wave Dynamics in a Fluid of Light
• Formation of dispersive shock waves in evolution of a two-temperature collisionless plasma
• Formation of dispersive shock waves in a saturable nonlinear medium
• Shock wave generation and propagation in dissipative and nonlocal nonlinear Rydberg media
• Plasma slab expansion into vacuum