Publication Cover
Applicable Analysis
An International Journal
Volume 45, 1992 - Issue 1-4
14
Views
3
CrossRef citations to date
0
Altmetric
Original Articles

Some connections between inverse scattering and solution hierarchies

Pages 19-47 | Published online: 02 May 2007

References

  • Ablowitz , M. and Segur , H. 1985 . Solitons and the inverse scattering transform , Philadelphia : SIAM .
  • Ablowitz , M. , Kaup , D. , Newell , A. and Segur , H. 1974 . Studies Appl. Math , 53 : 249 – 315 .
  • Adler , M. 1979 . Inventiones Math , 50 : 219 – 248 .
  • Asano , N. and Kato , Y. 1985 . Prog, Theor. Phys , 74 : 1005 – 1012 . 80 (1988), 774-792
  • Bergvelt , M. and ten Kroode , A. 1988 . Jour. Math. Phys , 29 : 1308 – 1320 .
  • R. Carroll, On some relations involving tau functions, dressing kernels, and spectral data, toappear
  • R. Carroll, Some remarks on the Hirota bilinear identity, to appear
  • R. Carroll, On the ubiquitous Gelfand-Levitan-Marcenko (GLM) equa-tion, Acta Applicandae Math., to appear
  • R. Carroll, On the determinant theme for tau functions, Grassman-nians, and inverse scattering, to appear
  • Carroll , R. and Delic , G. 1989 . Math. Methods Appl. Sci , 11 : 43 – 63 .
  • R. Carroll, Topics in soliton theory, In preparation
  • Carroll , R. 1988 . Mathematical physics , Amsterdam : North-Holland .
  • Carroll R. Some remarks on KP Proc. L.K. Hua Sympos. Beijing July 1988 to appear
  • Carroll , R. . Springer Lect. Notes Math . 1394 . Proc. Internat. Conf. Diff. Eqs. . pp. 11,134 – 17,141 . Ohio Univ. Press .
  • Carroll R. On the forced nonlinear Schrodinger equations Japan. Jour. Appl. Math. 1964 2 to appear
  • Carroll , R. . RIMS Kokyuroku 698 . Proc. 6 Sympos. Evol. Eqs. . pp. 94 – 101 . Kyoto .
  • Caudry , P. 1982 . Physica Vol. 6 , 51 – 66 .
  • Chadan , K. and Sabatier , P. 1977 . Inverse problems in quantum scattering theory , N.Y : Springer .
  • Date , E. , Kashiwara , M. , Jimbo , M. and Miwa , T. 1983 . RIMS Sympos., World Scientific 39 – 119 . Singapore
  • Dorfmeister , J. , Neher , E. and Szmigielski , J. 1989 . Quart. Jour. Math. Oxford , 40 : 161 – 195 .
  • Drinfeld , V. and Sokolov , V. 1984 . Contem. Prob. Math , 24 : 81 – 180 .
  • Faddeev , L. and Takhtajan , L. 1987 . Hamiltonian methods in the theory of solitons , N.Y : Springer .
  • Flaschka , H. , Newell , A. and Ratiu , T. 1983 . Physica Vol. 9 , 300,324 – 323,332 .
  • Flaschka , H. 1983 . Quart. Jour. Math. Oxford , 34 : 61 – 65 .
  • Helminck , G. and Post , G. 1988 . Lett. Math. Phys Vol. 16 , 359 – 364 .
  • Imbens , H. 1989 . Finite dimensional solutions of hierarchies of soliton equations , Utrecht : Proefschrift .
  • Kac , V. and Raina , A. 1987 . “ Highest weight representations of infinite dimensional Lie algebras ” . In World Scientific Singapore
  • Kato , Y. 1987 . Prog. Theor. Phys , 78 : 198 – 213 . 76 (1986), 768-783
  • Kato , Y. and Nakajima , N. 1986 . Prog. Theor. Phys , 76 : 981 – 998 .
  • Matsuno , Y. 1984 . Bilinear transformation method , N.Y : Academic Press .
  • Mc Kean , H. 1989 . Comm. Pure Appl. Math , 42 : 687 – 701 .
  • Mc Kean , H. 1979 . PDE and geometry , 237 – 254 . N.Y : Dekker .
  • Mc Kean , H. 1986 . Revista Mat. Iberoamericana , 2 : 235 – 261 . Jour. Statis. Phys., 46 (1987), 1115-1143
  • Mc Kean , H. and Ercolani , N. 1990 . Inventiones Math , 99 : 483 – 544 .
  • Mickelsson , J. 1989 . Current algebras and groups , N.Y : Plenum .
  • Mulase , M. 1989 . Advances Math.,54(1984), 57-66 , Vol. 2 , 473 – 492 . N.Y : Academic Press . Algebraic Anal
  • Newell , A. 1985 . Solitons in mathematics and physics , Philadelphia : SIAM .
  • Ohta , Y. , Satsuma , J. , Takahashi , D. and Tokihiro , T. 1988 . Prog. Theor. Phys., Supp , 94 : 210 – 241 .
  • Oishi , S. 1979,1980 . Jour. Phys. Soc. Japan , 47,48 : 1037,1341,349,639 – 1038,1346,350,646 .
  • Oishi , S. 1982 . Mem. School Sci. Engin., Waseda Univ , 46 : 191 – 225 .
  • Pöppe , Ch. 1989 . Inverse Probs , 5 : 613 – 630 .
  • Pöppe , Ch. and Sattinger , D. 1989 . Publ. RIMS, Kyoto Univ , 24 : 505 – 538 .
  • PÖppe , CH. 1984 . physica , 13 ( D ) : 137 – 160 .
  • Post , G. 1988 . “ KP hierarchies and reductions ” . In Algebraic and geometric aspects , Twente : Proefschrift .
  • Pressley , A. and Segal , G. 1986 . Loop groups , Oxford Univ. Press .
  • Segal , G. and Wilson , G. 1984 . Publ. IHES , 61 : 5 – 65 .
  • Symes , W. 1980 . Inventiones Math , 59 : 13 – 51 . Physica ID (1980), 339-374
  • ten Kroode , A. 1984 . CWI Syllabus
  • Wilson , G. . Phil. Trans. Royal Soc. London . Math. Proc. Cambridge Phil. Soc . Vol. 315 , pp. 393 – 404 . 86,131-143

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.