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Interactions of Dispersive Shock Waves



Mark Hoefer, Mark J. Ablowitz


Interactions and collisions of dispersive shock waves in defocusing (repulsive) nonlinear Schrodinger-type systems are investigated analytically and numerically. Two canonical cases are considered. In one case, two counter-propagating dispersive shock waves collide, interact, and eventually exit the interaction region with larger amplitudes and altered speeds. In the other case, a fast dispersive shock overtakes a slower one, giving rise to an interaction. Eventually, the two merge into a single dispersive shock wave. In both cases, the interaction region is described by a modulated, quasi-periodic two-phase solution of the nonlinear Schrodinger equation. The boundaries between the background density, dispersive shock waves, and their interaction region are calculated by solving the Whitham modulation equations. These asymptotic results are in excellent agreement with full numerical simulations. It is further shown that the interactions of two dispersive shock waves are directly analogous to the interactions of two classical shock waves, the only difference being the generation of an intermediate interaction region in the dispersive case.
Physica D-Nonlinear Phenomena


Bose-Einstein condensates, collisionless shock waves, dispersive shock waves, nonlinear optics, shock waves, zero dispersion limit


Hoefer, M. and Ablowitz, M. (2007), Interactions of Dispersive Shock Waves, Physica D-Nonlinear Phenomena, [online],, (Accessed May 26, 2024)


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Created August 1, 2007, Updated October 12, 2021