### Abstract:

The soliton concept has been established in several areas of applied science, and many of dynamical systems. The aim of this work is to use the theory of soliton to describe some physical phenomena concerning radiation and superconductivity. To achieve this aim, the researcher adopted the descriptive analytical approach.
In this thesis, by using link between the classical and quantum friction for harmonic oscillator soliton, the equation of harmonic oscillator soliton is constructed in the context of the quantum Schrodinger equation with frictional term. 0ne derives, for two solitons, solutions of the equation of the motion of a one-dimensional harmonic oscillator with frictional term and use them to obtain two different solitons types, one represents exponentially increasing beam, while the other stands for exponentially decreasing beam. The former is suitable for explaining lasing, while the later describes inelastic scattering. The Hamiltonian corresponding to these harmonic oscillator solitons lead to describe some physical systems. One could, however, make use of theoretical approach to quantize the classical motion using Hamiltonian, temperature, relaxation time, and crystal Potential. this indicates that the corresponding quantum systems are entirely different. The Harmonic Oscillator Soliton model describes the properties of two types of solitons, permanent and time dependent. The first one a bell soliton, has a permanent profile, while other one, the breathers, have an internal dynamic, with their shape oscillates in time. One also constructs a model describes quantum string imbedded in a frictional medium having uniform internal field, in the coordinate space. The solution represents position decaying amplitude of travelling wave soliton (optical soliton). This also describe inelastic scattering process Another Model is also suggested for Superconducting State by treat charge carriers in superconductor as oscillating string soliton. The resistance is determined in terms of real energy and current and treated as a sum of positive SC part and negative part. the material become superconductor with zero resistance when E0 is negative and the soliton is in the form of travelling wave of amplitude. This model explains why superconductivity is destroyed when a magnetic field is applied.