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| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 李志豪 | |
| dc.contributor.author | Ming-Chieh Chen | en |
| dc.contributor.author | 陳明傑 | zh_TW |
| dc.date.accessioned | 2021-06-13T04:34:28Z | - |
| dc.date.available | 2006-07-24 | |
| dc.date.copyright | 2006-07-24 | |
| dc.date.issued | 2006 | |
| dc.date.submitted | 2006-07-20 | |
| dc.identifier.citation | [1] Pashaev O.K. and Lee J.-H., Resonance solitons as black holes in Madelung fluid. Mod. Phys. Lett. A 17 1601-1619 (2002).
[2] Antonovskii L. K., Phys. Rev. E, 54 (1996) 6285. [3] L. Martina, O. K. Pashaev and G. Soliani, Integrable Dissipative Structures in the Gauge Theory of Gravity, Class. Quantum Grav. 14 (1997), 3179. [4] S. Jin, C. D. Levermore and D. W. McLaughlim, Comm. Pure Appl. Math. 52, 613(1999). [5] de Bloglie, L. Sur le possibilit’e de relier les ph’enom`enes d’interf`ere et de diffraction a`la th’eorie des quanta de lumi`ere. C. R. Acad. Sci.(Paris), 183 447448(1926). [6] Bohm, D. A suggested interpretation of the quantum theory in terms of ”hidden variables” I. Phys. Rev. 85, 166-179(1952). [7] Akhmanov, A., Sukhorukov A. P. and Khokhlov, R. V. Self-focussing and diffraction of light in a nonlinear medium, Soviet Physics Uspekhi, 93, 609636(1968). [8] Nelson E., Derivation of the Sch‥odinger equation from Newtonian mechanics. Phys. Rev. 150, 1079-1085(1966). [9] Salesi G., Spin and Madelung fluid. Mod. Phys. Lett. A 11, 1815-1823(1996). [10] Guerra, F. and Pusterla, M. A., A nonlinear Schr‥odinger equation and its relativistic generalization from basic principles.Lett. Nuovo Cimento 34, 351356(1982). [11] Rogers C. and Schief W. K., The resonant nonlinear Schr‥odinger equation via an integrable capillarity model. Il Phys. Nuovo Cimento 114, 1409-1412(1999). [12] Bertolami, O. Nonlinear connections to quantum mechanics from quantum gravity. Phys. Lett. A 154, 225-229(1991). [13] Curevivich, A. V. and Krylov, A. L. A shock wave in dispersive hydrodynamics. Sov. Phys. Dokl. 32, 73-74(1988). [14] Karpman V. I., Nonlinear Waves in Dispersive Media. Pergamon, Oxford,(1975). [15] Akhiezer, A. I. Plasma Electrodynamics, Pergamon, Oxford,(1975). [16] L. Martina, O. K. Pashaev and G. Soliani, Phys. Rev. D58 084025, (1998). [17] J.-H Lee, O.K. Pashave, C. Rogers, and W.K. Schief, The resonant nonlinear Schr‥odinger equation in cold plasama physics. Application of B‥acklund-Draboux transformations and superposition Principles, to appear in J. Plasma Physics. [18] J.-H Lee, O.K. Pashave, RNLS solitons with nontrivial boundary condition by Hirota method.preprint. [19] R. Jackiw, Teor. Mat. Fiz 92 404, (1992). [20] Hirota R., Exact solution of the Korteweg-de Vries equation for multiple collisions of solitons. Phys. Rev. Lett. 27 1192-1194 (1992). [21] Arnold V I and Avez A 1968 Ergodic Problems of Classical Mechanics.(New York: Benjamin) [22] Jackiw R 1984 Quantum Theory of Gravity ed S Chirstensen.(Bristol: Hilger) [23] Teitelboim C 1983 Phys. Lett. 126B 41 [24] Isler K and Trugenberger C A 1989 Phys. Rev. Lett. 63 834 [25] Chamseddine A H and Wyler D 1990 Nucl. Phys. B 340 595 [26] Montano D and Sonnenschein J 1989 Nucl. Phys. B 324 348 [27] Birmingham D, Blau M, Rakowski M and Thompson G 1991 Phys. Rep. 209 129 | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/33320 | - |
| dc.description.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. | en |
| dc.description.provenance | Made available in DSpace on 2021-06-13T04:34:28Z (GMT). No. of bitstreams: 1 ntu-95-R89221015-1.pdf: 547176 bytes, checksum: c6393d20aff43fb32948b7f4a389ac54 (MD5) Previous issue date: 2006 | en |
| dc.description.tableofcontents | 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 .............................................26 | |
| dc.subject | 毛細現象系統 | zh_TW |
| dc.subject | 廣田方法 | zh_TW |
| dc.subject | 反應擴散方程 | zh_TW |
| dc.subject | 共振薛丁格方程 | zh_TW |
| dc.subject | 冷電漿 | zh_TW |
| dc.subject | Resonant Nonlinear Schr | en |
| dc.subject | Cold plasma | en |
| dc.subject | Capillarity system | en |
| dc.title | 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 | zh_TW |
| dc.title | Nonlinear Schrodinger Equations with Quantum Potential and the Applications in Cold Plasma Equations | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 94-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 張秋俊,邵錦昌,蔡天鉞,李榮耀 | |
| dc.subject.keyword | 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, | zh_TW |
| dc.subject.keyword | Cold plasma,Capillarity system,Resonant Nonlinear Schr, | en |
| dc.relation.page | 27 | |
| dc.rights.note | 有償授權 | |
| dc.date.accepted | 2006-07-20 | |
| dc.contributor.author-college | 理學院 | zh_TW |
| dc.contributor.author-dept | 數學研究所 | zh_TW |
| 顯示於系所單位： | 數學系 | |
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