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| ???org.dspace.app.webui.jsptag.ItemTag.dcfield??? | Value | Language |
|---|---|---|
| dc.contributor.advisor | 李志豪(Jyh-Hao Lee) | |
| dc.contributor.author | Chuan-Hsing Kuo | en |
| dc.contributor.author | 郭傳興 | zh_TW |
| dc.date.accessioned | 2021-06-13T16:27:18Z | - |
| dc.date.available | 2005-07-15 | |
| dc.date.copyright | 2005-07-15 | |
| dc.date.issued | 2005 | |
| dc.date.submitted | 2005-07-15 | |
| dc.identifier.citation | [1] Bullough R. K., Caudrey(eds) P. J., Solitons, Topics in Current Physics, Springer-Verlag, 17,1980.
[2] Beals R., Coifman R. R., Scattering and inverse scattering for rst order systems, Comm. Pure Appl. Math., 37, 1984, No.1, pp.39-90. [3] Beals R., Coifman R. R., Inverse scattering and evolution equations, Comm. Pure Appl. Math., 38, 1985, No.1, pp.29-42. [4] Chang Chien-Hung, A special case of n n Zakharov-Shabat system, National Taiwan Univ. Master Thesis, 1990 [5] Degasperis A., Fordy A. P., and Lakshmanan M., Nonlinear evolution equations: integrability and spectral methods ,Manchester University Press, 1990 [6] Drazin P. G., Johnson R. S., Solitons: an Introduction, Cambridge University Press,1989 [7] Hietarinta J., Introduction to the Hirota bilinear method:Integrability of nonlinear system (Pondicherry 1996) , Lecture Notes in Physics,Springer-Verlag, Berlin, 495, 1997, pp.95-103. [8] Hirota R.,Direct methods in soliton theory,in Solitons, edited by R.K.Bullough and P.J.Caudrey,Springer-Verlag Berlin Heidelberg New York,1980. [9] Hirota R., Exact envelope-soliton solutions of a nonlinear wave equation, J. Math. Phys., 14(7), 1973. [10] Hirota R.,The direct method in soliton theory,Cambridge Tracts in Mathematics,155.Cambridge University Press,Cambridge,2004. [11] Kaup D.J., Newell A.C., An exact solution for a derivative nonlinear Schrodinger equation, J. Math. Phys. , 19(4), 1978, pp.789-801 [12] Lee Jyh-Hao, Global solvability of the derivative nonlinear Schrodinger equation, Transactions of the A.M.S., 314(1), 1989, pp.107-118. [13] Lee Jyh-Hao, Inverse scattering transform and D-bar method, National Science Council Report, 1990-1991 [14] Lee Jyh-Hao, Inverse scattering transform and Wavelets, National Science Council Report, 1991- 1992 [15] Lee Jyh-Hao, On the dissipative evolution equation associated with Zakharov-Shabat system with a quadratic spectral parameter, Transactions of A. M. S., 316(2), 1989, pp.327-336. [16] Lee Jyh-Hao, Solvability of the derivative nonlinear Schrodinger equation and the massive thirring model, Teoreticheskayai Matematicheskaya Fizika, 99(2), 1994, pp.322-328 [17] Lee Jyh-hao,Lee Yen-Ching,Lin Chien-Chih, Exact solutions of DNLS and the derivative Reaction-Diffusion System, to appear in J. of Nonlinear Math. Physics, Vol.9 (2002),Suppl. 1, 87- 98. Proc. of the Special Session on Integrable Systems of the First Joint Meeting of AMS-HKMS , Dec. 13-16, 2000, Hong Kong. [18] Lee Jyh-hao,Lee Yen-Ching,Lin Chien-Chih, Some exact solutions of DNLS and derivative Reaction-Diffusion systems via Hirota method, Proc. of 10th Workshop on Differential Equations, Chang-Hua Univ. of Education, Nov. 2-4, 2001. [19] Lee Yen-Ching, Exact solutions of the derivative nonlinear Schrodinger equation and the derivative reaction-diffusion system via Hirota bilnearization method, National Taiwan Univ. Master Thesis, Jan. 1999. [20] Lin Chao-Ting, One and two dimension inverse scattering transform and the associated evolution equations, National Taiwan Univ. Master Thesis, 1992 [21] Lin Chien-Chih, Exact solutions of the derivative reaction-di usion system via Hirota bilnearization method, National Taiwan Univ. Master Thesis, Jan. 2001 [22] Martina L., Pashaev O. K. and Soliani G., Integrable dissipative structures in the gauge theory of gravity, Classical Quantum Gravity, 14(12), 1997, pp.3179-3186. [23] Miwa T.,Jimbo M.,Date E., Solitons,Cambridge Tracts in Mathematics,135.Cambridge University Press,Cambridge,2000. [24] Nakamura A., Chen H.-H., Multi-soliton solutions of a derivative nonlinear Schr odinger equation, J. Phys. Soc. Japan, 49(2), 1980, pp.813-816 [25] Nakamura A., Hirota R., A new example of explode-decay solitary waves in one-dimension, J. Phys. Soc. Japan ,5(2), 1985, pp.491-499. [26] Pashaev O. K., Lee Jyh-Hao, and Lin Chi-Kun, Equivalence relation and bilinear representation for derivation nonlinear Schr odinger type equations, , Proc. of the Workshop on Nonlinearity, Integrability and All That-20 years after NEEDS'79, Gallipoli, Lecce, Italy, July 1-10, 1999 , pp. 175-181, World Scienti c, 2000. [27] Pashaev O. K., Lee Jyh-Hao, Self-dual vortices in chern-simons hydrodynamics, Theor. Math. Phys.127(2001)779-788 [28] Pashaev O. K., Lee Jyh-Hao, Integrability and Quantum potential from dissipatons to exponentially localized Chern-Simon solitons, Proc. of the Workshop on Nonlinearity, Integrability and All That-20 years after NEEDS'79, Gallipoli, Lecce, Italy, July 1-10, 1999 , pp. 479-503, World Scienti c, 2000. [29] Pashaev O. K., Lee Jyh-Hao, Black holes and solitons of quantized dispersionless NLS and DNLS equations, , to appear in ANZIAM J. of Applied Maths(continues of J. of Australian Mathematical Society, Ser. B:Applied Math.). [30] Pashaev O. K. and Lee Jyh-hao, Resonance solitons as black holes in Madelung uid, Modern Physics Letters A, Vol. 17, No. 24 (2002),1601-1619. [31] Pashaev O. K. and Lee Jyh-hao, Bilinear representation for the modi ed nonlinear Schr odinger equation and their quantum potential deformation, presented in the Workshop on Nonlinear Physics: Theory and Experimenst.II , Gallipoli(Lecce), Italy, June 27-July 6, 2002 [32] Pashaev O. K. and Lee Jyh-hao, Solitons resonances for MKP-II,presented in the Workshop on Nonlinear Physics:Theory and Experiments.II,Gallipolli(Lecce),Italy, June-July,2004 [33] Rogers,Colin ,private communication. [34] Shaw J.-C. and Yen H.-C., Solving DNLS equation by Riemann problem technique, Chinese J. of Mathematics, 18(3), 1990, pp.283-293. | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/38165 | - |
| dc.description.abstract | 本論文首先重述二階AKNS-ZS 系統之質譜問題及相關之進展方程。此方程之孤立子解可由退化之逆質譜變換求得，也可由Hirota 雙
線性法求得。 我們也重述具量子位能之NLS 及DNLS 與相關之反應擴散方程。我們也考慮混合型方程之情形。用Hirota 法求得1-dissipaton 解，這 已由Pashaev et al.求出[31]，我們於第三章3.3 節附上1-dissipaton 的函數圖。我們也求得2-dissipaton 解，就我們所知這結果是新的。 | zh_TW |
| dc.description.abstract | In this thesis, we will review some results on NLS and DNLS and the versions with 'quantum potential'. At first, we will review some results about two by two AKNS-ZS system with a linear and quadratic spectral parameter. Here exact solutions of NLS and DNLS could be obtained by degenerate inverse scattering transform, also by Hirota bilinearization method.
We also review the reaction-diffusion systems related to NLS with 'quantum potential' and derivative reaction-diffusion systems related to DNLS with 'quantum potential'. Here we consider the mixed type case called modified NLS with 'quantum potential'. Some exact solutions (e.g. one-dissipatons, two-dissipatons) of the related mixed type Reaction-Diffusion system(MDRD) are constructed by Hirot a bilinearization method. Some plots of the one-dissipatons are given in section 3. | en |
| dc.description.provenance | Made available in DSpace on 2021-06-13T16:27:18Z (GMT). No. of bitstreams: 1 ntu-94-R91221013-1.pdf: 1011995 bytes, checksum: da8f28e3f022abb16fc0b29bd94623c8 (MD5) Previous issue date: 2005 | en |
| dc.description.tableofcontents | Contents
1 Introduction . . . . . . . . . . . . . . . . . . . . . .1 2 Examples of nonlinear evolution equation from U-V condition . . . . . . . . . . . . . . . . . . . . . .2 2.1 Review on 22 AKNS-ZS system with a linear spectral parameter in Beals-Coifman set-up . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2.1.1 Scattering problem . . . . . . . . . . . . . . . . . . . . . . . . 2 2.1.2 Associated evolution equations . . . . . . . . . . . . . . . . . . . . . . . . 3 2.2 Review on 22 AKNS-ZS system with a quadratic spectral parameter . . . . . . . . . . . . . . . . . 3 2.2.1 Scattering problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.2.2 Associated evolution equations . . . . . . . . . . . . . . . . . . . . . . . . 4 2.3 Examples of 22 U-V equations with linear and quadratic spectral parameters . . . . . . . . . . . . . 4 2.4 Comparison of One-Soliton Solutions via Different Methods . . . . . . . . . . . . . . . . . . .6 3 NLS & DNLS with 'quantum potential' 8 3.1 DNLS with 'quantum potential' . . . . . . . . . . . . . . . . . . . . . . . 8 3.2 Modied NLS with 'Quantum Potential' . . . . . . . . . . . . . . . . . . . . . . 11 3.3 Some plots of exact solutions . . . . . . . . . . . . . . . . . . . . . . . 13 4 Conclusion . . . . . . . . . . . . . . . . . . 14 Appendix . . . . . . . . . . . . . . . . . . 15 A Equivalent Relations . . . . . . . . . . . . . . . . . 15 B Some computation results for the asymptotic expansion of MJM.......................................17 C Hirota Bilinear Method.......20 D Possible application (Colin Rogers' remarks).........21 D.1 Some equation in plasma.......................21 D.2 NLS with 'quantum potential'.............21 D.3 Reaction-Diffusion System related to NLS with 'quantum potential'..................22 Bibliography ..............................23 | |
| dc.language.iso | en | |
| dc.subject | 具微分項反應擴散方程 | zh_TW |
| dc.subject | 反應擴散方程 | zh_TW |
| dc.subject | NLS | en |
| dc.subject | Reaction-Diffusion Systems | en |
| dc.subject | Derivative Reaction-Diffusion Systems | en |
| dc.subject | DNLS | en |
| dc.title | 反應擴散方程及具微分項反應擴散方程之公式解及其應用 | zh_TW |
| dc.title | Some Exact Solutions of Reaction-Diffusion Systems and
Derivative Reaction-Diffusion Systems and the Application | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 93-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 張秋俊,李榮耀,邵錦昌,吳德琪 | |
| dc.subject.keyword | 反應擴散方程,具微分項反應擴散方程, | zh_TW |
| dc.subject.keyword | Reaction-Diffusion Systems,Derivative Reaction-Diffusion Systems,DNLS,NLS, | en |
| dc.relation.page | 24 | |
| dc.rights.note | 有償授權 | |
| dc.date.accepted | 2005-07-15 | |
| dc.contributor.author-college | 理學院 | zh_TW |
| dc.contributor.author-dept | 數學研究所 | zh_TW |
| Appears in Collections: | 數學系 | |
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| ntu-94-1.pdf Restricted Access | 988.28 kB | Adobe PDF |
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