Darboux transformation and soliton solutions for the coupled cubic-quintic nonlinear Schrِdinger equations in nonlinear optics

In this paper, by virtue of the Darboux transformation (DT) and symbolic computation, the quintic generalization of the coupled cubic nonlinear Schrِdinger equations from twin-core nonlinear optical fibers and waveguides are studied, which describe the effects of quintic nonlinearity on the ultrashort optical pulse propagation in non-Kerr media. Lax pair of the equations is obtained and the corresponding DT is constructed. Moreover, one-, two- and three-soliton solutions are presented in the forms of modulus. Features of solitons are graphically discussed: (1) head-on and overtaking elastic collisions of the two solitons; (2) periodic attraction and repulsion of the bounded states of two solitons; (3) energy-exchanging collisions of the three solitons.