Algebro-geometric Poisson Brackets for Real Finite-zone Solutions of the Sine-gordon Equation and the Nonlinear Schrödinger Equation

@inproceedings{Dubrovin2007AlgebrogeometricPB,
  title={Algebro-geometric Poisson Brackets for Real Finite-zone Solutions of the Sine-gordon Equation and the Nonlinear Schrödinger Equation},
  author={Boris Dubrovin and Sergei Petrovich Novikov},
  year={2007}
}
Algebro-geometric Poisson brackets for real, finite-zone solutions of the Korteweg–de Vries (KdV) equation were studied in [1]. The transfer of this theory to the Toda lattice and the sinh-Gordon equation is more or less obvious. The complex part of the finite-zone theory for the nonlinear Schrödinger equation (NS) and the sine-Gordon equation (SG) is analogous to KdV, but conditions that solutions be real require serious investigation. 

References

Publications referenced by this paper.
Showing 1-7 of 7 references

Dokl

B. A. Dubrovin
Akad. Nauk SSSR 265 (1982), 789; English transl. in Soviet Math. Dokl. 26 • 1982

Funktional

B. A. Dubrovin, S. M. Natanzon
Anal. i Priložen. 16 (1982), no. 1, 27; English transl. in Functional Anal. Appl. 16 • 1982
View 1 Excerpt

Modulations of sinh-Gordon and sine-Gordon wavetrains

M. G. Forest, D. W. McLaughlin
Preprint • 1982
View 1 Excerpt

Comm

H. P. McKean
Pure Appl. Math. 34 • 1981
View 1 Excerpt

Vestnik Leningrad

A. R. Its
Univ. 1976, no. 7 (Ser. Mat. Meh. Astr. vyp. 2), 39; English transl. in Vestnik Leningrad Univ. Math. 9 • 1981
View 2 Excerpts

Funkcional

O. I. Bogojavlenskĭı, S. P. Novikov
Anal. i Priložen. 10 (1976), no. 1, 9; English transl. in Functional Anal. Appl. 10 • 1976
View 1 Excerpt

Progr

H. Flaschka, D. W. McLaughlin
Theoret. Phys. 55 • 1976
View 1 Excerpt

Similar Papers

Loading similar papers…