李志豪臺灣大學：數學研究所陳明傑Chen, Ming-ChiehMing-ChiehChen2007-11-282018-06-282007-11-282018-06-282006http://ntur.lib.ntu.edu.tw//handle/246246/59450In 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.Introduction ............................................1 Chapter 1. Translate the cold plasma system into the resonant nonlinear Schr‥odinger equation................3 Chapter 2. Translate the capillarity system into the resonant nonlinear Schr‥odinger equation................6 Chapter 3. The Relation between RNLS and RD system.......8 Chapter 4. Exact Solutions of the Reaction-Diffusion system with Nonzero Boundary............................10 Chapter 5. Comparisons of one-soliton Solutions ........17 APPENDIX A. Exact Solutions of the Reaction-Diffusion system with Zero Boundary...............................20 APPENDIX B. A special two-dissipaton solution form via Hirota method with Nonzero Boundary.....................21 APPENDIX C. The Conserved Quantities....................23 APPENDIX D. Exact Solutions of Reaction-Diffusion system..................................................25 References .............................................26547176 bytesapplication/pdfen-US冷電漿毛細現象系統共振薛丁格方程反應擴散方程廣田方法Cold plasmaCapillarity systemResonant Nonlinear Schrthesishttp://ntur.lib.ntu.edu.tw/bitstream/246246/59450/1/ntu-95-R89221015-1.pdf