Abstract
This article recovers multiwave, homoclinic breather, M-shaped rational solitons and interaction of M-shaped rational solitons with single and double kinks for pure cubic nonlinear Schrodinger equation, with full nonlinearity, in a non-Kerr law media via the logarithmic transformation and symbolic computation with ansatz functions scheme. We use quadratic-cubic law and some suitable transformations involving trigonometric, exponential and hyperbolic functions to obtained various forms of stated solutions. In addition, we compute kink cross-rational solutions, periodic cross-rational solutions and periodic cross kink rational solutions for governing model. The proposed model is assumed with a few Hamiltonian perturbation terms that will sustain the balance between dispersion and self-trapping effect stemming from the nonlinear refractive index. Furthermore, the solitons behaviors for attained via different values parameters in the produced solutions are analyzed.