Resonating the Schrödinger equation with cubic-quintic-septic-nonic and quadrupled power-law nonlinearities: Analytical analysis and discussion

This paper extends the recent study by Samir et al. [Mathematics 10 (2022) 4085, doi:10.3390/math10214085] by exploring a broader class of nonlinear Schrödinger equations. It incorporates both cubic-quintic-septic-nonic and quadrupled power-law nonlinearities, along with a resonant term that plays a fundamental role in the propagation of optical solitons in optical systems. Additionally, a more sophisticated analytical method is employed, yielding infinite pairs of optical solitons for the extended class of resonant nonlinear Schrödinger equations. This study reveals that all results presented by Samir et al. [Mathematics 10 (2022) 4085, doi:10.3390/math10214085] are special cases of this work, alongside various existing studies that have now been generalized. Lastly, this study supports the findings of Samir et al. [Mathematics 10 (2022) 4085, doi:10.3390/math10214085] on the existence of optical solitons, showing that the integrability condition holds without requiring cubic and septic nonlinearities.