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研究生:林建志
研究生(外文):Lin, Chien-Chih
論文名稱:具微分項反應-擴散方程之耗散子解
論文名稱(外文):Dissipation Solutions of Derivative Reaction-Diffusion System via Hirota Bilinearization Method
指導教授:李志豪李志豪引用關係
指導教授(外文):Lee, Jhy-Hao
學位類別:碩士
校院名稱:國立臺灣大學
系所名稱:數學研究所
學門:數學及統計學門
學類:數學學類
論文種類:學術論文
論文出版年:2001
畢業學年度:89
語文別:英文
論文頁數:31
中文關鍵詞:
相關次數:
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在本篇論文我們用Hirota雙線性算子方法得到DNLS芳程的N-孤立子解,和反應擴散方程的N-耗散子解.反應擴散方程可以被轉換成DNLS方程加上量子位能(qantum potential)項.最後我們討論了有關1-耗散子和2-耗散子的行為.我們也用Mathematica軟體畫出一些耗散子之圖形.
In this thesis, we obtain N-solition solutions of DNLS equation, and N-dissipaton solutions of a Derivative Reaction-Diffusion equation(DRD) via Hirota Bilinearization Method. DRD can be transformed from DNLS plus "quantum potential" term. We
then discuss some behaviors about one dissipaton solutions and special two dissipaton solutions.We also show the figures of some dissipaton solutions by MATHEMATICA.
Ch1 Introdction 2
Ch2 Soliton Soltions of DNLS 3
2.1 1-Soliton Soltion of DNLS via Inverse Scattering
Transform 3
2.2 One and Two Soliton Solution of DNLS via Hirota''s
Bilinearization Method 5
2.3 Comparison of 1-Soliton Solutions among Different
Methods 6
2.4 Exact N-Soliton Solutions of DNLS 7
Ch3 N-Dissipaton Solutions of DRD System 11
Ch4 Behavior of Dissipaton 16
4.1 Behavior of One-Dissipaton 16
4.2 Behavior of Two-Dissipaton 17
4.3 Some Graphs of 2-Dissipaton Soltions 18
Ch5 Conclusion 19
[1]Mark J.Ablowitz and H.Segur, Solitons and the Inverse Scattering Transform, pp.171-191
[2]R. K. Bullough, P. J. Caudrey(eds), Solitons, Topics in Current Physics, Springer-Verlag, 17: (1980)
[3]Chien-Hung Chang, A special case of n*n Zakharov-Shabat
system, National Taiwan Rniv. Master
Thesis,:(1990)
[4]J.Hietarinta, Introduction to the Hirota bilinear method:Integrability of nonlinear system(pondicherry 1996), Lecture Notes in Physics, Springer-Verlag, Berlin}, 495:p.95-103(1997)
[5]Ryogo Hirota, J. Math. Phy. Vol. 14, (1973) 805.
[6]Ryogo Hirota, Journal of The Physical Society of Japan. Vol. 33,(1972) 1456.
[7]David J.Kaup and Alan C. Newell, An exact solution for a
derivative nonlinear Schrodinger equation, J.Math.Phys.p.798-801
1978
[8]Chao-Ting Lin, One and two dimesion inverse scattering transform
and the associated evolution equations, National Taiwan Rniv. Master Thesis,:(1992)
[9]Jyh-Hao Lee, Global solvability of the derivative nonlinear
Schrodinger equation,Transactions of hte
A.M.S.,314(1):p.107-118(1989)
[10]Jyh-Hao Lee, Solvability of the derivative nonlinear
Schrodinger equation and the massive thirring model,
Teoretecheskayai Matematecheskaya Fizida, 99(2):p.322-328(1994)
[11]Yen-Ching Lee, Exact solutions of the derivative
nonlinear Schrodinger equation and the derivative reaction-diffusion system via hirota bilinearization method, National Taiwan University Thesis,(1999).
[12]L.Martina, O.K. Pashaev and G.Soliani, Integrable dissipative structures in the gauge theory of gravity, Classical Quantum Gravity},14(12):p.3179-3186
[13]Akira Nakamura and Hsing-Hen Chen, Journal of The Physical
Society of Japan. Vol. 49, (1980) 813.
[14]O.K.Pashaev and Jyh-Hao Lee, Abelian Gauge Theory and Integrable Sigma Models, Lecture Note of Institute of Mathematics, Academia Sinica, Taiwan,1999.
[15]O.K.Pashaev and Jyh-Hao Lee, Black Holes and Solitons of
Quantized Dispersionless NLS and DNLS, to appear in ANIAM J. of Applied Maths.
[16]O.K.Pashaev and Jyh-Hao Lee, Resonance NLS Solitons as Black
Holes in Madelung Fluid, hep-th/9810139 v2 20 Oct 1998
[17]M.Remoissenet, Waves Called Solitons-Concepts and Experiments, pp.239-245
[18]J.C. Shaw and H.C. Yen, Solving DNLS equation by Riemann
problem technique, {\em Chinese J. of Mathematics}, 18(3):p.283-293(1990)
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