In this work, by applying the logarithmic transformation and symbolic computation with ansatz functions scheme, we examined the new solitons with carbon nanotube (CNT) as saturable absorbe (SA) in the ring-cavity fiber system. The system is renowned as a non-standard Schrodinger model through the coefficients combined real and imaginary numbers. We obtained Chirp-free soliton, Homoclinic breathers, M-shaped rational solitons, Multiwaves and their dynamics are revealed in plots by choosing the proper values of parameters. Additionally, four categories of interaction of M-shaped rational soliton with rogue wave, periodic wave and kink wave are studied. we accomplished the new structures and very fascinating interactional phenomena of M shaped soliton with kink waves. Furthermore, through a mixture of quadratic, cosine and hyperbolic transformations we obtained periodic cross rational (PCR) solutions and via three wave transformation we generated multiwave solutions.