Underdetermined systems of partial differential equations

Journal of Mathematical Physics

Volumn 41, Issue 9, 2000, Pages 6388-6398

  Bender, Carl M ^a   Dunne, Gerald V ^b   Mead, Lawrence R ^c  

^a WASHINGTON UNIVERSITY   (United States)

^b UNIVERSITY OF CONNECTICUT   (United States)

^c UNIVERSITY OF SOUTHERN MISSISSIPPI   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034345912     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.1287431     Document Type: Article

References (13)

1. There are special cases of complex linear differential equations whose general solutions have fewer arbitrary functions and there are even linear differential equations having no solutions whatsoever. [See P. R. Garabedian, Partial Differential Equations (Wiley, New York, 1964), pp. 450-455.] However, we will not consider such anomalous equations in this paper. Here, we are interested in equations that have more than the expected degree of arbitrariness.
2. We are using here the standard Einstein summation convention in which we sum over repeated indices.
3. C. M. Bender and D. H. Sharp, Phys. Rev. Lett. 50, 1535 (1983).
4. C. M. Bender and G. V. Dunne, Phys. Lett. B 200, 520 (1988).
5. C. M. Bender and G. V. Dunne, J. Math. Phys. 29, 1727 (1988).
6. C. M. Bender and G. V. Dunne, Phys. Rev. D 40, 2739 (1989).
7. C. M. Bender and G. V. Dunne, Phys. Rev. D 40, 3504 (1989).
8. C. M. Bender, K. Milton, D. H. Sharp, L. M. Simmons, Jr., and R. Stong, Phys. Rev. D 32, 1476 (1985).
9. C. M. Bender, K. A. Milton, S. S. Pinsky, and L. M. Simmons, Jr., Phys. Rev. D 33, 1692 (1986).
10. C. M. Bender, F. Cooper, K. A. Milton, S. S. Pinsky, and L. M. Simmons, Jr., Phys. Rev. D 35, 3081 (1987).
11. C. M. Bender, L. R. Mead, and K. Milton, Comput. Math. Appl. 28, 279 (1994).
12. C. M. Bender, L. R. Mead, and S. S. Pinsky, Phys. Rev. Lett. 56, 2445 (1986).
13. C. M. Bender, L. R. Mead, and S. S. Pinsky, J. Math. Phys. 28, 509 (1987).