The Kadomtsev-Petviashvili equation as a source of integrable model equations

Journal of Mathematical Physics

Volumn 37, Issue 12, 1996, Pages 6207-6212

  Maccari, Attilio ^a  

^a Istituto Tecnico G Cardano   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0030371074     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.531773     Document Type: Article

References (14)

1. W. Eckhaus, "The long-time behaviour for perturbed wave equations and related problems," preprint 404, Department of Mathematics, University of Utrecht, 1985, published in part in Springer Lecture Notes in Physics, 1986, Vol. 346.
2. F. Calogero and W. Eckhaus, "Necessary conditions for integrability of nonlinear PDEs," Inverse Prob. 3, L27-L32 (1987).
3. F. Calogero and W. Eckhaus, "Nonlinear evolution equations, rescalings, model PDEs and their integrability. I," Inverse Prob. 3, 229-262 (1987).
4. F. Calogero and W. Eckhaus, "Nonlinear evolution equations, rescalings, model PDEs and their integrability. II," Inverse Prob. 4, 11-33 (1988).
5. F. Calogero and A. Maccari, "Equations of nonlinear Schrodinger type in 1+1 and 2+1 dimensions obtained from integrable PDEs," P. C. Sabatier(editor): Inverse Problems: An Interdisciplinary Study, Proceedings of the Meeting on Inverse Problems, Montpellier, 1986, Advances in electronics and electron physics, edited by P. C. Sabatier (Academic, New York, 1988), Vol. 19, pp. 463-480.
6. F. Calogero and A. Maccari, "Equations of nonlinear Schrodinger type in 1+1 and 2+1 dimensions obtained from integrable PDEs," P. C. Sabatier(editor): Inverse Problems: An Interdisciplinary Study, Proceedings of the Meeting on Inverse Problems, Montpellier, 1986, Advances in electronics and electron physics, edited by P. C. Sabatier (Academic, New York, 1988), Vol. 19, pp. 463-480.
7. F. Calogero, "Why are certain nonlinear PDEs both widely applicable and integrable," in What is Integrability (For Nonlinear PDEs), edited by V. E. Zakharov (Springer-Verlag, New York, 1991).
8. A. Maccari, "The Boussinesq equation as a source of equations integrable by the spectral transform," submitted to Nonlinearity.
9. A. Maccari, "The nonlocal oscillator," accepted for publication in Nuovo Cimento B.
10. B. B. Kadomtsev and V. I. Petviashvili, "On the stability of solitary waves in weakly dispersive media," Sov. Phys. Dokl. 15, 539-541 (1970).
11. About the spectral transform, see for instance, F. Calogero and A. Degasperis, "Spectral transform and solitons," (North-Holland, Amsterdam, 1982).
12. E. I. Shulman, "On the integrability of equations of Davey-Stewartson type," Theor. Math. Phys. 56, 720-724 (1983).
13. A. Davey and K. Stewartson, "On three-dimensional packets of surface waves," Proc. R. Soc. London, Ser. A 338, 101-110 (1974).
14. D. Anker and N. C. Freeman, "On the soliton solutions of the Davey-Stewartson equation for long waves," Proc. R. Soc. London, Ser. A 360, 529-540 (1978).