Publication Cover
Applicable Analysis
An International Journal
Volume 64, 1997 - Issue 3-4
33
Views
6
CrossRef citations to date
0
Altmetric
Original Articles

The whitham equations revisited

The whitham equations revisited

Pages 343-378 | Received 01 Dec 1996, Published online: 02 May 2007

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

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.