具量子位能之非線性薛丁格方程與其在冷電漿方程上的應用

Abstract

In this paper, we first review the following results of C. Rogers et al: the cold plasma system under some physical constraints is related to Resonant Nonlinear Schr'{o}dinger Equation(RNLS) and the capillarity system under some chemical constraints is also related to RNLScite{roger}, cite{main}. The main result is to obtain one-dissipaton and two-dissipaton solution of the Reaction-Diffusion(RD) system with nonzero boundary condition via Hirota method. In one-dissipaton case, we make a comparison with the exact solutions derived from B'{a}cklund-Darboux transformation. The Reaction-Diffusion system is related to Resonant Nonlinear Schr'{o}dinger Equationcite{Lee}, which is related to a system of equations in cold plasma physics under special constraintscite{main}. Some plots of the resonant interaction are shown here.