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Differential equations for the Baker-Akhiezer functions of algebraic curves. (English) Zbl 0404.35030


MSC:

35J10 Schrödinger operator, Schrödinger equation
35G20 Nonlinear higher-order PDEs
35Q99 Partial differential equations of mathematical physics and other areas of application
35B99 Qualitative properties of solutions to partial differential equations

Citations:

Zbl 0385.35019
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References:

[1] I. M. Krichever, ”Integration of nonlinear equations by methods of algebraic geometry,” Funkts. Anal. Prilozhen.,11, No. 1, 15–31 (1977). · Zbl 0346.35028
[2] I. M. Gel’fand and L. A. Dikii, ”The resolvent and Hamiltonian systems,” Funkts. Anal. Prilozhen.,11, No. 2, 11–27 (1977).
[3] V. B. Matveev, ”Abelian functions and solutions,” Preprint No. 373, Inst. Fiz. Teor. Uniw. Wroclaw. (1976).
[4] B. A. Dubrovin, ”The periodic problem for the Korteweg–de Vries equation in the class of finite-zone potentials,” Funkts. Anal. Prilozhen.,9, No. 3, 41–51 (1975). · Zbl 0316.30019
[5] V. A. Andreev, FIAN Preprint No. 26 (1976).
[6] A. R. Its, ”Inversion of hyperelliptic integrals and integration of nonlinear differential equations,” Vestn. Leningr. Gos. Univ.,7, No. 2, 37–46 (1976). · Zbl 0336.35025
[7] V. O. Kozel and V. P. Kotlyarov, ”Almost-periodic solutions of the equation utt uxx + sin u = 0,” Dokl. Akad. Nauk Ukr. SSR, Ser. A,10, 878–881 (1976). · Zbl 0337.35003
[8] I. V. Cherednik, ”A method for obtaining operators almost commuting with a given operator,” Usp. Mat. Nauk,32, No. 5, 168 (1977).
[9] I. V. Cherednik, ”On a generalization of the KdV and sin-Gordon equations,” Funkts. Anal. Prilozhen.,12, No. 4 (1978). · Zbl 0369.14013
[10] O. R. Its and V. P. Kotlyarov, ”Explicit formulas for solutions of the nonlinear Schrödinger equation,” Dokl. Akad. Nauk Ukr. SSR,11, Ser. A, 965–968 (1976). · Zbl 0341.35050
[11] Yu. I. Manin, ”Algebraic aspects of nonlinear differential equations,” in: Contemporary Problems in Mathematics, Progress in Science and Technology [in Russian], VINITI, Moscow (1978), pp. 5–152.
[12] M. A. Shubin, ”Algebraic aspects of the theory of pseudodifferential operators and the Lax equations,” VINITI Abstract No. 157, deposited 10/II 1978.
[13] A. Neveu and N. Papanicolaou, ”Integrability of the classical [ \([\bar \psi _i \psi _i ]_2^2 and [\bar \psi _i \psi _i ]_2^2 - [\bar \psi _i \gamma _5 \psi _i ]_2^2\) interactions,” preprint, Inst. Advanced Study, Princeton.
[14] J. L. Burchnall and T. W. Chaundy, ”Commutative ordinary differential operators,” Proc. R. Soc. London, Ser. A,118, 557–583 (1928). · JFM 54.0439.01
[15] H. F. Baker, ”Note on the foregoing paper ’Commutative ordinary differential operators’ by J. L. Burchnall and T. W. Chaundy,” Proc. R. Soc. London, Ser. A,118, 584–593 (1928). · JFM 54.0439.02
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