Traveling Wave Solutions of the Kawahara Equation Joining Distinct Periodic Waves

Sprenger, Patrick; Bridges, Thomas J.; Shearer, Michael

doi:10.1007/s00332-023-09922-0

Cited by 4 publications

(1 citation statement)

References 44 publications

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“…While the mathematical theory for Dispersive Shock Waves (DSWs) in local media is wellestablished and developed, the same cannot be said for nonlocal media. Physical examples of nonlocal media include shallow waters with surface tension (capillary effect) [48,49,50,51,52], polarized light waves in defocusing nematic liquid crystals [46,47,74,75], femtosecond pulses in nonlinear fiber optics [76], photorefractive crystals [79] and thermal optical media [77,78].…”

Section: Dispersive Shock Waves Modulation Theory and Non-convex Disp...mentioning

confidence: 99%

Nematic Dispersive Shock Waves from Nonlocal to Local

et al. 2021

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The structure of optical dispersive shock waves in nematic liquid crystals is investigated as the power of the optical beam is varied, with six regimes identified, which complements previous work pertinent to low power beams only. It is found that the dispersive shock wave structure depends critically on the input beam power. In addition, it is known that nematic dispersive shock waves are resonant and the structure of this resonance is also critically dependent on the beam power. Whitham modulation theory is used to find solutions for the six regimes with the existence intervals for each identified. These dispersive shock wave solutions are compared with full numerical solutions of the nematic equations, and excellent agreement is found.

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