Krichever, I. M. Elliptic solutions of the Kadomtsev-Petviashvili equation and integrable systems of particles. (English) Zbl 0473.35071 Funct. Anal. Appl. 14, 282-290 (1981). Translation from Funkts. Anal. Prilozh. 14, No. 4, 45–54 (1980; Zbl 0462.35080). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 2 ReviewsCited in 74 Documents MSC: 35Q53 KdV equations (Korteweg-de Vries equations) 35Q58 Other completely integrable PDE (MSC2000) 37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) 37K20 Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with algebraic geometry, complex analysis, and special functions 37K15 Inverse spectral and scattering methods for infinite-dimensional Hamiltonian and Lagrangian systems Keywords:elliptic solutions; Kadomtsev-Petviashvili equation; integrable systems of particles; Lax-type representation; inverse problem method; Hamiltonian Citations:Zbl 0462.35080 PDF BibTeX XML Cite \textit{I. M. Krichever}, Funct. Anal. Appl. 14, 282--290 (1981; Zbl 0473.35071) Full Text: DOI OpenURL References: [1] H. Bateman and A. Erdelyi, Higher Transcendental Functions. Elliptic and Automorphic Functions, LamĂ© and Mathieu Functions [Russian translation], Nauka, Moscow (1967). [2] F. Calogero, ”Exactly solvable one-dimensional many-body systems,” Lett. Nuovo Cimento,13, 411-415 (1975). [3] A. M. Perelomov, ”Completely integrable classical systems connected with semisimple Lie algebras,” Lett. Math. Phys.,1, 531-540 (1977). [4] H. Airault, H. McKean, and J. Moser, ”Rational and elliptic solutions of the KdV equation and related many-body problem,” Commun. Pure Appl. Math.,30, 95-125 (1977). · Zbl 0338.35024 [5] I. M. Krichever, ”Rational solutions of the Kadomtsev?Petviashvili equation and integrable systems of N particles on a line,” Funkts. Anal. Prilozhen.,12, No. 1, 76-78 (1978). · Zbl 0374.70008 [6] D. V. Choodnovsky and G. V. Choodnovsky, ”Pole expansions of nonlinear partial differential equations,” Nuovo Cimento,40B, 339-350 (1977). · Zbl 0324.02066 [7] F. Calogero, ”Integrable many-body problem,” Preprint, Univ. di Roma, No. 89 (1978). · Zbl 0399.70022 [8] K. M. Case, ”The N-soliton solutions of the Bendgamine?Ono equation,” Proc. Nat. Acad. Sci. USA,75, 3562-3563 (1978). · Zbl 0449.35085 [9] M. A. Olshanetsky and A. M. Perelomov, ”Explicit solutions of some completely integrable systems,” Lett. Nuovo Cimento,17, 97-133 (1976). · Zbl 0342.58017 [10] M. A. Olshanetsky and N. V. Rogov, ”Bound states in completely integrable systems with two types of particles,” Ann. Inst. H. Poincare,29, 169-177 (1978). · Zbl 0416.58014 [11] D. V. Choodnovsky, ”Meromorphic solutions of nonlinear partial differential equations and particle integrable systems,” J. Math. Phys.,20, No. 12, 2416-2424 (1979). · Zbl 0455.35096 [12] V. S. Dryuma, ”An analytic solution of the two-dimensional Korteweg?de Vries equation,” Pis’ma Zh. Eksp. Teor. Fiz.,19, No. 12, 219-225 (1973). [13] V. E. Zakharov and A. B. Shabat, ”A scheme for the integration of nonlinear equations of mathematical physics by an inverse problem of scattering theory. I,” Funkts. Anal. Prilozhen.,8, No. 3, 43-53 (1974). · Zbl 0303.35024 [14] E. Kamke, Handbook on Ordinary Differential Equations [in German], Chelsea Publ. [15] I. M. Krichever, ”An algebraic-geometric construction of the Zakharov?Shabat equations and their periodic solutions,” Dokl. Akad. Nauk SSSR,227, No. 2, 291-294 (1976). · Zbl 0361.35007 [16] I. M. Krichever, ”The integration of nonlinear equations by the methods of algebraic geometry,” Funkts. Anal. Prilozhen.,11, No. 1, 15-31 (1977). · Zbl 0346.35028 [17] H. Baker, ”Note on the foregoing paper, ?Commutative ordinary differential equations,?” Proc. R. Soc. London, Ser. A,118, 570-576 (1928). [18] B. A. Dubrovin and S. P. Novikov, ”Periodic and conditionally periodic analogues of many-soliton solutions of the Korteweg?de Vries equation,” Zh. Eksp. Teor. Fiz.,67, No. 12, 2131-2143 (1974). This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.