On optical Airy beams in integrable and non-integrable systems

• Interaction of Airy beams and solitary waves in local and nonlocal media investigated.
• Integrable and non-integrable equations considered.
• Bäcklund transformation used for integrable equation.
• Interaction in a nematic liquid crystal without and with birefringent walkoff analysed.
• In the absence of walkoff, no momentum exchange between solitary wave and Airy beam.

The interaction of an accelerating Airy beam and a solitary wave is investigated for integrable and non-integrable equations governing nonlinear optical propagation in various media. For the integrable nonlinear Schrödinger equation, by way of a Bäcklund transformation, we show that no momentum exchange takes place, as the only effect of the interaction is to modulate the amplitude of the solitary wave. The latter result also holds for propagation in anisotropic media with birefringent walkoff and nonlocality, as specifically addressed with reference to uniaxial nematic liquid crystals in the absence of beam curvature. When the wavefront curvature characteristic of accelerating Airy beams is accounted for, both asymptotic and numerical solutions show that a small amount of momentum is initially exchanged, with the solitary wave rapidly settling to a state of constant momentum.