Abstract
In this paper, the weakly nonlinear wave propagation theory in the occurrence of magnetic fields in fluids of superposed is studied. The amplitude evolution of governing equations of the amplitude of the progressive waves is reported. The soliton and other kinds solutions of (2+1)-dimensional elliptic nonlinear Schrödinger equation is constructed. We also investigate the properties of envelope of the (2+1)-dimensional wave pocket. The propagation of pulses ahead of ultra-short range in the optical communication systems is illustrated by this dynamical equation. The modified and extended rational expansion method is utilized for obtaining different kinds of wave solutions such as bright-dark solitons, solitons of Kink and anti-Kink, solitary waves, periodic solutions and elliptic function solutions of this equation. These achieved exact solutions are further general and useful to researcher for understanding physical phenomena. Several solutions are novel by comparing these solutions with existing solutions. The power and effectiveness of current can observed form constructed solutions.