The whitham equations revisited: The whitham equations revisited

Applicable Analysis

Volumn 64, Issue 3-4, 1997, Pages 343-378

  Carroll, Robert ^a   Chang, Jen Hsu ^a  

^a NONE

Author keywords

Averaging; Baker akhiezer function; Dispersionless kp; Kp equations; Lax operator; Riemann surface; Seiberg witten theory; Symplectic geometry; Whitham equations

Indexed keywords

EID: 0010871250     PISSN: 00036811     EISSN: 1563504X     Source Type: Journal    
DOI: 10.1080/00036819708840541     Document Type: Article

References (78)

1. Adler, M., and vanMoerbeke, P., 1992. Comm. Math. Phys., 147: 25–56. Comm. Pure Appl. Math., 47(1994), 5-37
2. Martinez Alonso, L., and Moreno, E., 1995. Chaos, solitons, and fractals, 5: 2213–2237.
3. Aoyama, S., and Kodama, Y., 1994. Mod. Phys. Lett. A, 9: 2481–2492. hep-th 9505122
4. Baker, H., 1897. Abelian functions, Cambridge Univ. Press.
5. Belokolos, E., Bobenko, A., Enolskij, V., Its, A., and Matveev, V., 1994. Algebro-geometric approach to nonlinear integrable equations, Springer.
6. Bilal A., hep-th 9601007
7. Bloch, A., and Kodama, Y., 1992. SIAM Jour. Appl. Math., 52: 909–928.
8. Bonelli G., Matone M., hep-th 9605090
9. Carroll, R., 1991. Topics in soliton theory, North-Holland.
10. Carroll, R., 1993. Applicable Anal., 49: 1–31. 56 (1995), 147-164
11. Carroll, R., 1995. Proc. First World Cong. Nonlinear Analysts, Vol. 1, 241–252. Berlin: deGruyter.
12. Carroll, R., and Kodama, Y., 1995. Solution of the dispersionless Hirota equations. Jour. Phys. A, 28: 6373–6387. hep-th 9506007
13. Carroll, R., 1994. Jour. Nonlin. Sci., 4: 519–544. Teor. Mat. Fizika, 99 (1994), 220-225
14. Carroll, R., 1995. Proc. NEEDS 94. World Scientific, 4: 24–33.
15. Carroll R., solv-int 9511009 Nauka
16. Carroll R., Qi-nian Jin, solv-int 9606005, Proc. Second World Congress Nonlinear Analysts Athens, North-Holland1996 to appear
17. Carroll R., hep-th 9607219, Mod. Phys. Lett. 1996 to appear
18. Carroll R., Some kernels on a Riemannn surface 1996 to appear
19. Carroll R., Qi-nian Jin, Lecture notes on Kdv, KP, Toda, TFT, susy, integrability, Riemann surfaces, matrix models, LG and SW theories, etc., 542 pages Univ. of Illinois Urbana 1995-1996
20. Carroll R., ep-th 9610216
21. Cherednik I., Basic methods of solition theory World Scientific 1996
22. D'Hoker E., Krichever I., Phong D., hep-th 9609041, 9609145, and 9610156
23. Dijkgraaf, R., Verlinde, H., and Verlinde, E., 1991. Nucl. Phys. B, 352: 59–86.
24. Donagi, R., and Witten, E., 1996. Nucl. Phys. B, 460: 299–334.
25. Dubrovin, B., and Novikov, S., 1989. Russ. Math. Surv., 44: 35–124.
26. Dubrovin, B., 1983. Dokl. Akad. Nauk. SSSR, 27: 665–669.
27. Dubrovin, B., 1981. Russ. Math. Surv., 36: 11–92.
28. Dubrovin, B., Krichever, I., and Novikov, S., 1982. Math. Phys. Rev., 3: 1–150.
29. Dubrovin, B., and Novikov, S., 1991. Math. Phys. Rev., 9: 3–136.
30. Dubrovin, B., 1982. Math. USSR., 19: 285–296. Izvestia
31. Dubrovin, B., 1995. “ Integrable systems and quantum groups ”. In Lecture notes in math., Vol. 1620, 120–348. Springer.
32. Dubrovin, B., 1992. Nucl. Phys. B, 379: 627–689.
33. Dubrovin, B., 1992. Comm. Math. Phys., 145: 195–207.
34. Eguchi, T., and Yang, S., 1996. Mod. Phys. Lett. A, 11: 131–138.
35. Farkas, H., and Kra, I., 1992. Riemann surfaces, Springer.
36. Fay, J., 1973. Theta functions on Riemann surfaces. Springer Lect. Notes Math., 352
37. Flaschka, H., Forest, M., and McLaughlin, D., 1980. Comm. Pure Appl. Math., 33: 739–784.
38. Forster, O., 1992. Lectures on Riemann surfaces, Springer.
39. Forest, M., and McLaughlin, D., 1983. Stud. Appl. Math., 68: 11–59. SIAM Jour. Appl. Math., 44 (1984), 287-300
40. Fucito, F., Gamba, A., Martellini, M., and Ragnisco, O., 1992. Inter. Jour. Mod. Phys. B, 6: 2123–2147.
41. Gibbons, J., and Kodama, Y., 1994. Singular limits of dispersive waves, 61–66. Plenum.
42. Griffiths, P., 1989. Introduction to algebraic curves, Amer. Math. Soc.
43. Grinevich, P., Orlov, A., and Schulman, E., 1993. Important developments in soliton theory, 283–301. Springer.
44. Itoyama H., Morozov A., hep-th 9511126, 9512161, and 9601168
45. Kawamoto, N., Namikawa, Y., Tsuchiya, A., and Yamada, Y., 1988. Comm. Math. Phys., 116: 247–308.
46. Klemm, A., Lerche, W., and Theisen, S., 1996. Inter. Jour. Nod. Phys. A, 11: 1929–1973.
47. Kodama, Y., and Gibbons, J., 1990. Proceedings Fourth Workshop on Nonlinear and Turbulent Processes in Physics. World Scientific, 11: 166–180.
48. Kodama Y., Lecture Lyon workshop 1991 unpublished
49. Kodama, Y., and Gibbons, J., 1989. Phys. Lett. A, 135: 167–170.
50. Kodama, Y., 1988. Phys. Lett. A, 129: 223–226. Prog. Theor. Phys. Supp. 94 (1998), 184-194
51. Krichever, I., 1988. Funct. Anal. Prilozh., 22: 200–213.
52. Krichever, I., 1989. Russ. Math. Surv., 44: 145–225.
53. Krichever, I., 1995. Acta Math. Applicandae, 39: 93–125.
54. Krichever, I., 1991. Math. Phys. Rev., 9: 1–103.
55. Krichever, I., 1986. Funct. Anal. Prilozh., 20: 203–214.
56. Krichever, I., 1994. Comm. Pure Appl. Math., 47: 437–475.
57. Krichever, I., 1992. Comm. Math. Phys., 143: 415–429.
58. Krichever I., Phong D., hep-th 9604199
59. Krichever I., hep-th 9611158
60. Lax, P., Levermore, C., and Venakides, S., 1993. Important developments in soliton theory, 205–241. Springer.
61. Maltsev A., solv-int 9611008
62. Marshakov A., Mironov A., Morozov A., hep-th 9607109
63. Martinec E., Warner N., 1996 hep-th 9509161
64. Matone, M., 1995. Phys. Lett. B, 357: 342–348. hep-th 9506181
65. Matsukidaira, J., Satsuma, J., and Strampp, W., 1990. Jour. Math. Phys., 31: 1426–1434.
66. McLaughlin, D., 1981. Physica 3D, 31: 335–343.
67. Mumford D., Lectures on theta, 1 and 2, Birkhäuser, 1983-84
68. Nakatsu T., Takasaki K., hep-th 9509162
69. Novikov, S., Manakov, S., Pitaevskij, L., and Zakharov, V., 1984. Theory of Solitons, Plenum.
70. Seiberg, N., and Witten, E., 1994. Nucl. Phys. B, 426: 19–52.
71. Sonnenschein J., Yankielowicz S., Theisen S., hep-th 9510129
72. Springer, G., 1981. Introduction to Riemann surfaces, Chelsea.
73. Takasaki K., Nakatsu T., hep-th 9603069
74. TakasakI, k., and TakebE, T., 1995. Inter. Jour. Mod. Phys. A, Supp. 1992, pp. 889-922;. Rev. Math.Phys, 7: 743–808.
75. Takasaki K., Nakatsu T., hep-th 9603069
76. Venakides, S., 1985. Comm. Pure Appl. Math., 38: 125–155. and 883-909; Trans. Amer. Math. Soc., 301 (1987), 189-226; Comm. Pure Appl. Math., 42 (1989), 711-728; Comm. Pure Appl. Math., 43 (1990), 335-361
77. Verlinde, E., and Verlinde, H., 1987. Nucl. Phys. B., 288: 357–396.
78. Whitham, G., 1974. Linear and nonlinear waves, Wiley.