On Huygens' principle for dirac operators and nonlinear evolution equations

Journal of Nonlinear Mathematical Physics

Volumn 8, Issue SUPPL., 2001, Pages 62-68

  Chalub, Fabio A C C ^a   Zubelli, Jorge P ^a  

^a IMPA   (Brazil)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0039781170     PISSN: 14029251     EISSN: None     Source Type: Journal    
DOI: 10.2991/jnmp.2001.8.s.12     Document Type: Conference Paper

References (16)

1. Hadamard J, Lectures on Cauchy's Problem in Linear Partial Differential Equations, Yale University Press, New Haven, 1923.
2. Günther P, Huygens' Principle and Hadamard's Conjecture, The Mathematical Intelligencer, 1991, V.13, N 2, 56-63.
3. Courant R and Hilbert D, Methods of Mathematical Physics, Vol. I-II, Interscience Publishers, Inc, New York, 1953.
4. Berest Y and Veselov A, Huygens' Principle and Integrability, Russian Mathematical Surveys, 1994, V.49, N 6, 5-77.
5. Stellmacher K L, Ein Beispiel einer Huyghensschen Differentialgleichung, Nachr. Akad. Wiss. Göttingen. Math. Phys. Kl. Math.-Phys. Chem. Abt., 1953, V.1953, 133-138.
6. Lagnese J E and Stellmacher K L, A Method of Generating Classes of Huygens' Operators, J. Math. Mech., 1967, V.17, N 5, 461-472.
7. Lagnese J E, A Solution of Hadamard's Problem for a Restricted Class of Operators, Amer. Math. Soc., 1968, V.19, 981-988.
8. Adler M and Moser J, On a Class of Polynomials Connected with the KdVEquations, Comm. Math. Phys., 1978, V.61, N 1, 1-30.
9. Zubelli J P, Topics on Wave Propagation and Huygens' Principle, Lecture Notes Published in the 21st Brazilian Mathematical Colloquium, ISBN 85-244-0131-1, http://www.impa.br/-zubelli.
10. Dirac P A M, The Quantum Theory of the Electron, Proc. Roy. Soc. of London A, 1928, V.117, 610-624.
11. Thaller B, The Dirac Equation, Springer-Verlag, Berlin, 1992.
12. Folland G B, Fundamental Solutions for the Wave Operator, Exposition. Math., 1997, V.15, N 1, 25-52.
13. Gardner C S, Greene J M, Kruskal M D and Miura R M, Method for Solving the Korteweg-de Vries Equation, Phys. Rev. Lett., 1967, V.19, 1095-1097.
14. Calogero F and Degasperis A, Spectral Transform and Solitons, North-Holland, Amsterdam, 1982.
15. Burchnall J L and Chaundy T W, A Set of Differential Equations that Can Be Solved by Polynomials, Proc. Lond. Math. Soc., 1929/30, V.30, 401-414.
16. Berest Y and Loutsenko I M, Huygens' Principle in Minkowski Spaces and Soliton Solutions of the Korteweg-de Vries Equation, Comm. Math. Phys., 1997, V.190, N 1, 13-132.