Bright and dark solitons of a weakly nonlocal Schrodinger equation involving the parabolic law nonlinearity

The search for soliton solutions of nonlocal Schrodinger equations in the presence of nonlinear effects has received special interest in the last few decades. In the present paper, a weakly nonlocal Schrodinger equation (WNSE) involving the parabolic law nonlinearity is considered and as a success, its soliton solutions including bright and dark solitons are constructed. Such a key goal is formally carried out using a series of efficient approaches such as Kudryashov and exponential methods (Their new versions). The results presented in this paper are of a significant role to describe the propagation of soliton waves in the weakly nonlocal parabolic law medium.