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A full analysis of all regimes for optical dispersive shock wave (DSW)propagation in nematic liquid crystals is undertaken. These dispersive shockwaves are generated from step initial conditions for the optical field and areresonant in that linear diffractive waves are in resonance with the DSW,resulting in a resonant linear wavetrain propagating ahead of it. It is foundthat there are six regimes, which are distinct and require different solutionmethods. In previous studies, the same solution method was used for allregimes, which does not yield solutions in full agreement with numericalsolutions. Indeed, the standard DSW structure disappears for sufficiently largeinitial jumps. Asymptotic theory, approximate methods or Whitham modulationtheory are used to find solutions for these resonant dispersive shock waves ina given regime. The solutions are found to be in excellent agreement withnumerical solutions of the nematic equations in all regimes. It is found thatfor small initial jumps, the resonant wavetrain is unstable, but that itstabilises above a critical jump height. It is additionally found that the DSWis unstable, except for small jump heights for which there is no resonance andlarge jump heights for which there is no standard DSW structure.

Modulation theory and resonant regimes for dispersive shock waves in nematic liquid crystals