Abstract
The solitons and other solutions illustrate nondiffractive and nondispersive spatiotemporal localized packets of wave propagating in the media of optical Kerr. In this paper, solitons, elliptic function and other solutions of dimensionless time-dependent paraxial wave model are constructed via employing three mathematical techniques, namely, the improved simple equation technique, exp(-Phi(zeta)-expansion technique and modified extended direct algebraic technique. These wave solutions have key applications and help to understand the physical phenomena of this wave model. By giving appropriate parameter values, different types of solitons structures can be depicted graphically. Several precise solutions and computations have proved the straightforwardness, consistency and power of the these techniques.