Nikan Ahmadi Karchi - School of Mathematics and Computer Science, Iran University of Science and Technology, Narmak, Tehran ۱۶۸۴۶-۱۳۱۱۴, Iran
mohammad bagher ghaemi - School of Mathematics and Computer Science, Iran University of Science and Technology, Narmak, Tehran ۱۶۸۴۶-۱۳۱۱۴, Iran
Javad Vahidi - School of Mathematics and Computer Science, Iran University of Science and Technology, Narmak, Tehran, Iran.

This paper studies advanced mathematical methods like sin-cos and sinh-cosh approachesto find precise solutions by considering inter-modal dispersion and spatio-temporal dynamics with kerrlaw nonlinearity in the Resonant shrödinger equation. These methods are useful for solving nonlinearpartial differential equations. To obtain the ordinary differential equation for the traveling wave solution,we initially deal with the general partial differential equation (PDE). Then, a series of optical solitonsolutions, including cusp and dark solitons, are derived for the Resonant shrödinger equation using thiseffective approach.

sine-cosine and sinh-cosh methods, solition solution with complex structure, Resonant nonlinear Schrodinger equation, Optics