Integrable Dynamics of Charges Related to the Bilinear Hypergeometric Equation

Communications in Mathematical Physics

Volumn 242, Issue 1-2, 2003, Pages 251-275

  Loutsenko, Igor ^a  

^a SISSA   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0242592947     PISSN: 00103616     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00220-003-0944-z     Document Type: Article

References (22)

1. Adler, M., Moser, J.: On a class of polynomials connected with the Korteveg-de Vries equation. Comm. Math. Phys. 61, 1-30 (1978)
2. Aref, H.: Integrable, Chaotic and turbulent motion of vortices in two dimensional flows. Ann. Rew. Fluid Mech. 15, 345-389 (1983)
3. Arnold, V.I., Khesin, B.A.: Topological Methods in Hydrodynamics. NY: Springer-Verlag, 1998
4. Bartman, A.B.: A new interpretation of the Adler-Moser KdV polynomials: interaction of vortices. Nonlinear and Turbulent Processes in Physics, Vol. 3 (Kiev 1983), Chur: Harwood Academic Publ., 1984, pp. 1175-1181
5. Berest, Y.: Huygens principle and the bispectarl problem. CRM Proceedings and Lecture Notes 14, 1998
6. Berest, Y., Loutsenko, I.: Huygens principle in Minkowski space and soliton solutions of the Korteveg de-Vries equation. Commun. Math. Phys. 190, 113-132 (1997)
7. Burchnall, J.L., Chaundy, T.W.: A set of differential equations which can be solved by polynomials. Proc. London Math. Soc. 30, 401-414 (1929)
8. Calogero, F.: Motion of poles and zeros of special solutions of nonlinear and linear partial differential equations and related "solvable" many body problems. Nuovo Cimento 43 B, 177 (1978)
9. Chalych, O., Feigin, M., Veselov, A.: Multidimensional Baker-Akhieser Functions and Huygens Principle. Commun. Math. Phys. 206, 533-566 (1999)
10. Choodnovsky, D., Choodnovsky, G.: Pole expansions of nonlinear partial differential equations. Nuovo Cimento 40 B, 339 (1977)
11. Crum, M.: Associated Sturm-Liouville Systems. Quart. J. Math 6, 121-127 (1955)
12. Gurevich, B.B.: Foundations of the Theory of Algebraic Invariants. Groningen, Holland: P. Noordhoff, 1964
13. Hadamard, J.: Lectures on Cauchy's Problem in Linear Partial Differential Equations. New Haven, CT: Yale Univ. Press, 1923
14. Heckman, G.J., Opdam, E.M.: Root systems and hypergeometric functions I. Composite Math. 64 329-352 (1987)
15. Inozemtsev, V.: On the motion of classical integrable systems of interacting particles in an external field. Phys. Lett. 98, 316-318 (1984)
16. Krichever, I.: Methods of algebraic geometry in the theory of nonlinear equations. Russ. Math. Surv. 32, 185-213 (1977)
17. Krichever, I.: Rational solutions of the Kadomtsev-Petviashvilli equation and integrable systems of N particles on line. Funct. Anal. Appl. 12, 76-78 (1978)
18. Novikov, S., Pitaevski, L., Zakharov, V., Manakov, S.: Theory of Solitons: Inverse Scattering Method. New York, NY: Contemporary Soviet Mathematics, 1984
19. Perelomov, A.M.: Integrable Systems in Classical Mechanics and Lie's Algebras. Moscow: Nauka 1990
20. Szegö, G.: Orthogonal Polynomials. NY: AMS, 1939
21. Turbiner, A.V.: Quasi-exactly solvable problems and sl(2) algebra. Commun. Math. Phys. 118, 467 (1988)
22. Veselov, A.: Rational solutions of the Kadomtsev-Petviashvilli equation and Hamiltonian systems. Russ. Math. Surv. 35, 239-240 (1980)