Stability Theory of Nonlinear Waves

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9703695 Strauss The purpose of this project is to study mathematical models of waves that occur in the theories of plasmas, of fluids, and of other branches of physical science. Stability and instability phenomena will be investigated, particularly in the kinetic theory of charged particles with and without collisions. Stability problems for a variety of other kinds of waves, including breathers, solitary waves and dispersive waves, will also be explored. Energy conserving waves of marginal stability will be emphasized, and methods of mathematical analysis will be employed in the investigations. Waves occur in many forms in the physical environment, such as in the ocean, the atmosphere, biochemical processes, acoustics, telecommunications, and so on. The most complicated ones are the nonlinear ones, where it is difficult to predict the outcomes without very complex calculations. Some of these nonlinear waves are unstable, which means that a small change creates a large disturbance. Which waves are stable and which are unstable will be the focus of this project. The basic principles for understanding these phenomena are mathematical. These principles are fundamental to the creation of high-performance computing algorithms. We shall investigate the stability theory especially within the theory of physical plasmas. The stability of nonlinear plasma waves is relevant to such diverse applications as fusion energy research and satellite and radio communications in space.