This dissertation investigates and describes the concept of soliton and shock formation in plasma. A rigorous theoretical investigation is made to find energy of EASWs in unmagnetized collisionless plasma. By employing reductive perturbation method, KdV equation is derived for kappa and Cairns distributed electrons. HPM technique is used to handle KdV equation. The consequences of different parameters ? (spectral index) and ? = ??/?? on soliton profile are discussed. Secondly, soliton and shock formation is studied in a magnetized rotating plasma using Cairns distribution. An admitted solitary wave solution KdV equation and an admitted travelling wave solution KdVB equation are derived. HPM technique is applied on derived KdV equation and ???ℎ-method on derived KdVB equation. It is noticed that ? = ?ℎ/??, ? = ?0?/?0ℎ affect both the soliton width and amplitude. It is also noticed that ? = ??/??, ? = ?0?/?0ℎ, kinematic viscosity and angular frequency affect the structure of shocks. Thirdly, solitons in ion-temperaturegradient (ITG) mode in a plasma are studied. Using Braginskii’s model, KdV equation in ITG mode is derived. Dependence of soliton width and amplitude on parameters ?? = ??/ ??, ? = ?? /??, and ?0 is discussed. After that, solitons formation is studied in electron-temperaturegradient (ETG) mode in a plasma. Using Braginskii’s model linear dispersion relation and KdV equation for the ETG mode are derived. It is observed that the ETG mode supports only rarefactive solitons. It is also observed that soliton profile is sensitive to ? = ??/??, ?? = ??/?? and ?0. As finding of the connection of entropy with density and temperature of plasmas gives an incitement to investigate different entropy based plasma models. Therefore, using Braginskii’s model dispersion relation and KdV for ITG mode in presence of entropy drift are derived. It is noticed only compressive solitons can be generated in this mode. It is found that entropy enhances soliton amplitude and width. It is also found that in presence of entropy drift increasing magnetic field and ion temperature enhance the soliton profile. Lastly, nonlinear dissipative one and twodimensional structures (shocks) are investigated in nonuniform magnetized plasma with respect to entropy. The dissipation comes in the medium through ion-neutral collisions. Linear dispersion relation is derived. KdVB and KPB equations are derived for nonlinear drift waves in 1-D and 2- D by employing the drift approximation. It is found that ??/? plays a significant role in the shocks formation. It is noticed that ??/? determines the rarefactive and compressive nature of the shocks. It is observed upper and lower bounds exist for the shocks velocity. It is also observed that the existing regimes for both one and two-dimensional shocks for kappa distributed electrons are different from shocks with Cairns distributed electrons. Both rarefactive and compressive shocks are found for the 1-D drift waves with kappa distributed electrons. Interestingly, it is noticed that entropy enhances the strength of one and two-dimensional shocks.