The nonlinear chirp solitons are for the first time derived in optical nanofibers, thus illustrating the set of confined structure with nontrivial phase for the model of Schrödinger–Hirota equation. The model is studied with the dispersion of self-phase and self-steeping coefficients. The results show that bright, dark and singular solitons are dependent on the pulse intensity. Additionally, the constraint settings for the existence of solitons are also fall out during the derivation.
The current research deals with the exact solutions of the nonlinear partial differential equations having two important difficulties, that is, the coefficient singularities and the stochastic function (white noise). There are four major contributions to contemporary research. One is the mathematical analysis where the explicit a priori estimates for the existence of solutions are constructed by Schauder’s fixed point theorem. Secondly, the control of the solution behavior subject to the singular parameter ϵ when ϵ → 0. Thirdly, the impact of noise that is present in the differential equation has been successfully handled in exact solutions. The final contribution is to simulate the exact solutions and explain the plots.
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