A new integrable Davey-Stewartson-type equation

Journal of Mathematical Physics

Volumn 40, Issue 8, 1999, Pages 3971-3977

  Maccari, Attilio ^a  

^a Istituto Tecnico G Cardano   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0033241164     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.532937     Document Type: Article

References (23)

1. F. Calogero and W. Eckhaus, 26quot;Necessary conditions for integrability of nonlinear PDEs," Inverse Probl. 3, L27-L32 (1987).
2. F. Calogero and W. Eckhaus, "Nonlinear evolution equations, rescalings, model PDEs and their integrability. I," Inverse Probl. 3, 229-262 (1987).
3. F. Calogero and W. Eckhaus, "Nonlinear evolution equations, rescalings, model PDEs, and their integrability. II," Inverse Probl. 4, 11-33 (1988).
4. F. Calogero and A. Maccari, "Equations of nonlinear Schrodinger-type in 1 + 1 and 2+1 dimensions obtained from integrable PDE," "Inverse problems: An interdisciplinary study," in 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.
5. 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, Berlin, 1991).
6. A. Maccari, "Dissipative hidimensional systems and resonant excitations," Int. J. Nonlinear Mech. 33, 713-726 (1998).
7. A. Maccari, "Approximate solution of a class of nonlinear oscillators in resonance with a periodic excitation," Nonlinear Dynamics 15, 329-343 (1998).
8. A. Davey and K. Stewartson, "On three-dimensional packets of surface waves," Proc. R. Soc. London, Ser. A 338, 101-110 (1974).
9. 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).
10. A. Maccari, "The Kadomtsev-Petviashvili equation as a source of integrable model equations," J. Math. Phys. 37, 6207-6212 (1996).
11. A. Maccari, "The Boussinesq equation as a source of equations integrable by the spectral transform," Nonlinearity 10, 849-856 (1997).
12. A. Maccari, "A generalized Hirota equation in 2 + 1 dimensions," J. Math. Phys. 39, 6547-6551 (1998).
13. A. Maccari, "A model equation for nonresonant interacting ion acoustic plasma waves," J. Plasma Phys. 60, 275-288 (1998).
14. A. Maccari, "Nonresonant interacting ion acoustic waves in a magnetized plasma," J. Phys. A 32, 693-709 (1999).
15. B. Konopelchenko and V. Dubrovsky, "Some new integrable nonlinear evolution equations in 2 + 1 dimensions," Phys. Lett. 102A, 15-17 (1984).
16. B. Konopelchenko, Introduction to Multidimensional Integrable Equations (Plenum, New York, 1992).
17. Z. Jiang and R. K. Bullough, "Combined ∂̄ and Riemann-Hubert inverse methods for integrable nonlinear evolution equations in (2 + 1) dimensions,̄ J. Phys. A 20, L429-L435 (1987).
18. Z. Jiang, "Construction of scattering data for a class of multidimensional scattering operators," Inverse Probl. 5, 349-374 (1989).
19. A. S. Fokas, "On the simplest integrable equation in 2 + 1," Inverse Probl. 10, L19-L22 (1994).
20. E. I. Shul'man, "On the integrability of equations of Davey-Stewartson-type," Theor. Math. Phys. 56, 720-724 (1984).
21. A. S. Fokas and P. M. Santini, "Recursion operators and bi-Hamiltonian structures in multidimensions. I," Commun. Math. Phys. 115, 375-419 (1988).
22. F. Pempinelli, M. Boiti, and P. C. Sabatier, "First and second order nonlinear evolution equations from an inverse spectral problem," Inverse Probl. 9, 1-37 (1993).
23. A. Folguera, "Davey-Stewartson-type equations of the second and third order: Derivation aid classification," J. Math. Phys. 39, 2947-2968 (1998).