A continuum limit of the Toda Lattice

Memoirs of the American Mathematical Society

Volumn , Issue 624, 1998, Pages 1-216

  Deift, P ^a   McLaughlin, K T R ^a  

^a NONE

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0031616564     PISSN: 00659266     EISSN: None     Source Type: Journal    
DOI: 10.1090/memo/0624     Document Type: Article

References (23)

1. [1] R. W. Brockett. Dynamical Systems that Sort Lists, Solve linear Programming Problems and Diagonalise Symmetric Matrices. Proceedings of the IEEE Conference on Decision and Control, 1988.
2. [2] R. W. Brockett and A. M. Bloch. Sorting With the Dispersionless Limit of the Toda Lattice. preprint, 1990.
3. [3] V. Buslaev and A. Fedotov. Complex WKB Method for Harper's Equation. Preprint, 1992/93.
4. [4] O. Costin. Preprint, 1994.
5. [5] P. Deift, S. Venakides, and X. Zhou. private communication.
6. [6] H. Flaschka. On the Toda Lattice II. Prog. Theor. Phys., 51(3):703-716, 1974.
7. [7] H. Flaschka. The Toda Lattice. I. Existence of Integrals. Phys. Rev., B9:1924-1925, 1974.
8. [8] J. Geronimo and D. Smith. WKB Analysis of Second Order Difference Equations and Applications. Journal of Approximation Theory, 69(3):269-301, 1992.
9. [9] J. Goodman and P. Lax. On Dispersive Difference Schemes I. Comm. Pure. Appl. Math., 41:591-613, 1988.
10. [10] T. Hou and P. Lax. Dispersive Approximations in Fluid Dynamics. Comm. Pure. Appl. Math., 44:1-40, 1991.
11. [11] Y. Kodama. Solutions of the dispersionless Toda equation. Physics Letters A, 147(8,9):477-482, 1990.
12. p Spaces. LMS Lecture Notes 40, 1980.
13. [13] P. D. Lax and C. D. Levermore. The Small Dispersion Limit of the Korteweg -de Vries Equation I, II, III. Comm. Pure Appl. Math., 36:253-290, 571-593, 809-829, 1983.
14. [14] S. V. Manakov. Complete Intergrability and Stochastization of Discrete Dynamical Systems. Zh. Exp. Teor. Fiz., 67:543-555, 1974.
15. [15] K. D. T.-R. McLaughlin. A Continuum Limit of the Toda Lattice. Ph. D. Dissertation, New York University, 1994.
16. [16] J. Moser. Finitely Many Mass Points on the Line Under the Influence of an Exponential Potential - An Integrable System. Springer, New York, 1975.
17. [17] F. Olver. Introduction to Asymptotics and Special Functions. Academic Press, New York, 1974.
18. [18] G. Szego. Orthogonal Polynomials. AMS Colloquium Publications, v. 23, 1939.
19. [19] F. Tian. Oscillations of the Zero Dispersion Limit of the Korteweg de Vries Equation , (preprint). Comm. Pure Appl. Math., 1993.
20. [20] S. Tsarev. On Piosson Brackets and One - Dimensional Systems of Hydrodynamic Type. Sov. Math. Doklady, 31:488-491, 1985.
21. [21] S. Venakides. The Zero Dispersion Limit of the Korteweg - de Vries Equation With Periodic Initial Data. AMS Trans., 301:189-225, 1987.
22. [22] S. Venakides, P. Deift, and R. Oba. The Toda Shock Problem. Comm. Pure Appl. Math., 44:1171-1242, 1991.
23. [23] G. Whitham. Linear and Nonlinear Waves. J. Wiley, 1974.