Vector soliton molecules and their interactions for the coupled cubic-quintic nonlinear Schrödinger system in a non-Kerr medium: asymptotic behaviors.

Soliton molecules can enhance information capacity through multi-dimensional coding and provide an efficient data transmission way compared with traditional single-hump solitons in nonlinear optical fiber communication. The multi-hump solitons and their asymptotic behaviors of the coupled cubic-quintic nonlinear Schrödinger equation are studied, which illustrates the influence of the quintic nonlinearity on the ultrashort optical pulse propagation in the medium. On the vanishing background, we deduce the -soliton solutions. Based on those solutions, we present the proportional and disproportionate vector multi-hump solitons associated with the two, three, and four spectral parameters, and investigate their physical properties such as velocity and amplitude. Then, performing asymptotic analysis on soliton solutions of  = 3 and  = 4, we find that the exact solutions and asymptotic solutions show a clear consistency. When  = 3, we exhibit both asymptotically and graphically the transformation between the soliton molecules and single-, double-hump solitons before and after the interaction. When  = 4, we show the elastic or inelastic interactions among three different types of solitons: between double-hump solitons, between the soliton molecules and single solitons, the soliton molecules are controled by four spectral parameters. Moreover, we reveal that although the soliton's shape changes during the interaction, its intensity is not redistributed between the two components.