跳到主要內容

臺灣博碩士論文加值系統

(75.101.211.110) 您好!臺灣時間:2022/01/26 12:26
字體大小: 字級放大   字級縮小   預設字形  
回查詢結果 :::

詳目顯示

: 
twitterline
研究生:陳彩蓉
研究生(外文):Tsi-Jung Chen
論文名稱:長短波的交互作用
論文名稱(外文):On Short an Long Waves Interaction
指導教授:方永富
指導教授(外文):Yung-fu Fang
學位類別:碩士
校院名稱:國立成功大學
系所名稱:數學系應用數學碩博士班
學門:數學及統計學門
學類:數學學類
論文種類:學術論文
畢業學年度:90
語文別:英文
論文頁數:32
外文關鍵詞:Nonlinear Schrodinger EquationSemiclassical limit
相關次數:
  • 被引用被引用:0
  • 點閱點閱:190
  • 評分評分:
  • 下載下載:21
  • 收藏至我的研究室書目清單書目收藏:1
First,we use two different methods to get four conservation laws of the nonlinear Schrodinger equation. And then the local existence in time of the classical solutions can be established via an iteration method and the uniqueness of the solution is also proved. At last we prove the existence of the semiclassical limit of the solution.
1.Introduction 3
2.Hydrodynamics Structure and Conservation Laws 5
3.Modified Madulung Transformation 10
[1] D. J. Benney, A general theory for interactions between short and long waves, Stud. Appl. Math., 56, 81--94, 1977.
[2] T. Colin and A. Soyeur, Some singular limits for evolutionary Ginzburg Landau equations, Asymptotic Analysis, 13, 361--372, 1996.
[3] T. Colin and D. Lannes, Long-wave short-wave resonance for nonlinear geometric optics, Duke Math. Journal, 107, 351--419, 2001.
[4] C. Dafermos, Hyperbolic Conservation Laws in Continuum Physics, Grundlehren der mathematischen Wissenschaften Vol. 325, Springer, 2000.
[5] B. Desjardins, C. K. Lin and T. C. Tso, Semiclassical limit of the derivative nonlinear Schr"odinger equation, Math. Models Methods Appl. Sci., 10, 261--285, 2000.
[6] B. Desjardins and C. K. Lin, On the semiclassical limit of the general modified NLS equation, J. Math. Anal. Appl., 260, 546--571, 2001.
[7] V. D. Djordjevic and L. G. Redekopp, On two-dimensional packets of capillary-gravity waves, J. Fluid Mech., 79, 703--714, 1977.
[8] I. Gasser, C. K. Lin and P. Markowich, A review of dispersive limit of the (non)linear Schr"odinger-type equation, Taiwanese J. of Mathematics., 4, 501--529, 2000.
[9] E. Grenier, Semiclassical limit of the nonlinear Schr"odinger equation in small time, Proc. Amer. Math. Soc., 126, 523--530, 1998.
[10] C. H. Hsu and C. K. Lin, Convergence of the Godunov scheme for the modified Euler equation, preprint.
[11] J. S. Jiang and C. K. Lin, Homogenization of the Dirac-like system,
Math. Models Methods Appl. Sci., 11, 433--458, 2001.
[12] S. Jin, C. D. Levermore and D. W. McLaughlin, The semiclassical limit of the defocusing NLS hierarchy, Comm. Pure Appl. Math., 52, 613--654, 1999.
[13] C. Kenig, G.Ponce and L. Vega, Oscillatory integrals and regularity of dispersive equations, Indiana Univ. Math. J., 40, 33--67, 1991.
[14] P. Laurencot, On a nonlinear Schr"odinger equation arising in the theory of water wave, Nonlinear Analysis, Theory, Methods & Applications, 24, 509--527, 1995.
[15] J. H. Lee and C. K. Lin, The behavior of solutions of NLS equation of derivative type in the semiclassical limit, Chaos, Solitons & Fractals, 13, 1475--1492, 2002.
[16] H. L. Li and C. K. Lin , Semiclassical limit and well-posedness of Schr"odinger-Poisson and quantum hydrodynamics, preprint (2002).
[17] C. K. Lin,
Singular limit of the modified nonlinear Schr"odinger equation,
In: Nonlinear Dynamics and Renormalization Group, Edited by I. M. Sigal and C. Sulem, CRM Proceeding & Lecture Note Vol. 27, pp. 97--109, Amer. Math. Soc. 2001.
[18] Y. C. Ma, The complete solution of the long wave-short wave resonance equations, Stud. Appl. Math., 59, 201--221, 1978.
[19] T. Ogawa, Global well-posedness and conservation laws for the water wave interaction equation, Proceeding of the Royal Society of Edinburgh, 127A, 368--384, 1997.
[20] N. Sepulveda, Solitary waves in the resonant phenomenon between
a surface gravity wave packet and an internal gravity wave, Phys. Fluids, 30, 1984--1992, 1987.
[21] C. Sulem and P.-L. Sulem,
The Nonlinear Schrodinger Equation, Appl. Math. Sci. 139, Springer-Verlag, (1999).
[22] M. Tsutsumi and S. Hatano, Well-posedness of the Cauchy problem for the long wave-short wave resonance equations, Nonlinear Analysis, Theory, Methods & Applications, 24, 155--171, 1994.
[23] V. E. Zakharov and A. B. Shabat, Exact theory of two-dimensional self-focusing and one-dimensional self-modulation of waves in nonlinear media,
Soviet Phys. Jetp, 34, 62--69, 1972.
連結至畢業學校之論文網頁點我開啟連結
註: 此連結為研究生畢業學校所提供,不一定有電子全文可供下載,若連結有誤,請點選上方之〝勘誤回報〞功能,我們會盡快修正,謝謝!
QRCODE
 
 
 
 
 
                                                                                                                                                                                                                                                                                                                                                                                                               
第一頁 上一頁 下一頁 最後一頁 top