Unique soliton solutions to the nonlinear Schrödinger equation with weak non-locality and cubic–quintic–septic nonlinearity in nonlinear optical fibers

In this article, we will introduce new types of private soliton solutions to the higher order nonlinear Schrödinger equation (HOSE), containing cubic–quintic–septic nonlinearity, weak nonlocal nonlinearity, self-frequency shift, and self-steepening effect. The suggested model describes the propagation of an optical pulse in the weakly nonlocal nonlinear parabolic law media. We will derive these new types of soliton solutions in the framework of impressive, effective technique, namely, the Riccati–Bernoulli Sub-ODE method (RBSODM) which is one of the well-known ansatz methods that does not surrender to the homogeneous balance theory, reduce the volume of calculations and continuously achieves distinct results. In addition, to confirm and clarify our achieved results we will explore the identical numerical solutions for all realized soliton solutions using the Haar–Wavelet Method (HWM). The Haar–Wavelet Method that usually achieves good results is considered one of the recent numerical schemas. The 2D, 3D figures simulations between the soliton solutions and the numerical solutions have been demonstrated. The obtained soliton solutions are new when it compared with Zhou et al. (Chin Phys Lett 39: 044202, 2022) who solved this model by other technique.