Linear and nonlinear phenomena in semiconductor plasma like medium have been discussed in this thesis. The first chapter starts with the brief account of plasma related media, waves in plasma, methods of treating weak nonlinearity and basic phenomena of parametric instability and ion-implantation. All of these have been employed in the research papers included in this thesis. In the second chapter the phenomena of stimulated Brillouin scattering (SBS) has been examined in an un-magnetized piezoelectric semiconductor using quantum- hydrodynamic (QHD) model. It is seen that Bohm potential plus Fermi pressure have significantly improved the growth rate of stimulated Brillouin scattering. It is further noted that the improvement in the growth rate of stimulated Brillouin scattering occurs at higher values of electron number density and wave number of electron-acoustic wave. The third chapter concerns with the detailed study of shielding static potential and oscillating far-field potential in an ion- implanted piezoelectric semiconductor. In this ion- implanted piezoelectric semiconductor the colloid ions act as test particles. The quantum effect introduced via Bohm potential associated with electrons and the electron-coupling effect, both contribute to the dielectric response function of semiconductor. The tighter binding of the electrons is noted because of the presence of quantum effect due to which the length of effective wake potential and radius of quantum Debby shielding both are found to be reduced. As a result, the formation of quasi-quantum lattice of colloid ions in semiconductor is reported on quantum scale. The formation of such quasi-quantum lattice can cause thorough changes in the properties of ion- implanted semiconductor. In forth chapter we deal with a composite medium and study the propagation of nonlinear coupled helicon-spin and Alfven-spin waves through the composite medium. Composite medium is a medium which exhibits the properties of both semiconductors and magnetic materials. Using reductive perturbation technique we find the nonlinear evolution equations for these coupled waves which are found to have soliton solutions. The limiting cases for the semiconducting and magnetic materials have also been discussed separately in this chapter. In the last chapter our medium of research is gaseous dusty plasma. We have investigated analytically the nonlinear decay instability of dust-acoustic wave (DAW) and low-frequency electromagnetic wave in a collision-less dusty plasma which is homogeneous as well as magnetized. We have derived the nonlinear response function for the plasma particles using coupled fluid and Maxwell’s equations and developed un-damped growth rate for three-wave parametric decay instability. It is found that in magnetized dusty plasma, a large amplitude dust-acoustic wave undergoes a considerable decay. The growth rate of the instability is found to be highly sensitive to the externally applied magnetic field, ion number density and electron/ion temperature etc. A vibrant application of this work has also been identified in the environment of dusty plasma in space. The references are in the end of the thesis.