Trigonometric shock waves for the Kaup-Boussinesq system

Abstract

We consider the modulationally stable version of the Kaup-Boussinesq system which models propagation of nonlinear waves in various physical systems. It is shown that the Whitham modulation equations for this model have a new type of solutions which describe trigonometric shock waves. In the Gurevich-Pitaevskii problem of evolution of an initial discontinuity, these solutions correspond to a non-zero wave excitation on one of the sides of the discontinuity. Our analytical results are confirmed by numerical calculations.

References in corpus (4)

• Gurevich-Pitaevskii problem and its development
• Evolution of initial discontinuities in the Riemann problem for the Kaup-Boussinesq equation with positive dispersion
• Solution of the Riemann problem for polarization waves in a two-component Bose-Einstein condensate
• Localized structures on librational and rotational travelling waves in the sine-Gordon equation