From Agmon-Kannai expansion to Korteweg-de Vries hierarchy

Letters in Mathematical Physics

Volumn 49, Issue 1, 1999, Pages 71-77

  Polterovich, Iosif ^a  

^a WEIZMANN INSTITUTE OF SCIENCE   (Israel)

Author keywords

Heat invariants; Korteweg de Vries hierarchy

Indexed keywords

EID: 0041637384     PISSN: 03779017     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1007652006810     Document Type: Article

References (20)

1. Agmon, S. and Kannai, Y.: On the asymptotic behavior of spectral functions and resolvent kernels of elliptic operators, Israel J. Math. 5 (1967), 1-30.
2. Avramidi, I. G. and Schimming, R.: A new explicit expression for the Korteweg-de Vries hierarchy, solv-int/9710009.
3. Berger, M.: Geometry of the Spectrum, Proc. Sympos. Pure Math. 27, Amer. Math. Soc., Providence, 1975, pp. 129-152.
4. Fulling, S. A. (ed.): Heat Kernel Techniques and Quantum Gravity, Discourses Math. Appl. 4, Texas A&M Univ., College Station, 1995.
5. Gelfand, I. M. and Dikii, L. A.: Asymptotic behaviour of the resolvent of Sturm-Liouville equation and the algebra of the Korteweg-de Vries equations, Russian Math. Surveys 30(5) (1975), 77-113.
6. Gilkey, P.: Heat Equation Asymptotics, Proc. Symp. Pure Math. 54, Amer. Math. Soc., Providence, 1993, pp. 317-326.
7. Grandstein, I. S. and Ryzhik, I. M.: Table of Integrals, Series and Products, Academic Press, New York, 1980.
8. Its, A. R. and Matveev, V. B.: Hill's operator with finitely many gaps, Funct. Anal. Appl. 9(1) (1975), 65-66.
9. Its, A. R. and Matveev, V. B.: Schrödinger operator with finite-zonal spectrum and N-soliton solutions of the Korteweg-de Vries equation, Teoret. Mat. Fiz. 23(1) (1975), 51-68 (Russian).
10. Kruskal, M. D. Miura, R. M., Gardner, C. S. and Zabusky, N. J.: Korteweg-de Vries equation and generalizations, V. Uniqueness and nonexistence of polynomial conservation laws, J. Math. Phys. 11(3) (1970), 952-960.
11. McKean, H. P. and van Moerbeke, P.: The spectrum of Hill's equation, Invent. Math. 30 (1975), 217-274.
12. Miura, R. M., Gardner, C. S. and Kruskal, M. D.: Korteweg-de Vries equation and generalizations, II. Existence of conservation laws and constants of motion, J. Math. Phys. 9(8) (1968), 1204-1209.
13. Novikov, S. P.: The periodic problem for the Korteweg-de Vries equation, Funct. Anal. Appl. 8(3) (1974), 236-246.
14. Novikov, S. P.: Role of integrable models in the development of mathematics, In: M. Atiyah and D. Iagolnitzer (eds), Lectures of Fields Medalists, World Scientific, Singapore, 1997, pp. 202-218.
15. Novikov, S. P., Manakov, S. V., Pitaevskii, L. P. and Zakharov, V. E.: Theory of Solitons: the Inverse Scattering Method, Consultants Bureau, 1984.
16. I. Polterovich, Commutator method for computation of heat invariants, to appear in Indag. Math. (N.S.).
17. Rida, S. Z.: Explicit formulae for the powers of a Schrödinger-like ordinary differential operator, J. Phys. A: Math. Gen. 31 (1998), 5577-5583.
18. Schimming, R.: An explicit expression for the Korteweg-de Vries hierarchy, Acta Appl. Math. 39 (1995), 489-505.
19. Wolfram, S.: Mathematica: a System for Doing Mathematics by Computer, Addison-Wesley, Second edition, 1991.
20. Zakharov, V. E. and Faddeev, L. D.: Korteweg-de Vries equation: a completely integrable Hamiltonian system, Funct. Anal. Appl. 5(4) (1971), 20-287.