Lax pairs and Darboux transformations for Euler equations

Studies in Applied Mathematics

Volumn 111, Issue 1, 2003, Pages 101-113

  Li, Yanguang ^a   Yurov, Artyom V ^b  

^a UNIVERSITY OF MISSOURI   (United States)

^b NONE

Author keywords

[No Author keywords available]

Indexed keywords

DARBOUX TRANSFORMATIONS; EULER'S EQUATION; INVISCID FLUIDS; LAX PAIRS;

EULER EQUATIONS;

EID: 1842460740     PISSN: 00222526     EISSN: None     Source Type: Journal    
DOI: 10.1111/1467-9590.t01-1-00229     Document Type: Article

References (21)

1. 2, Part 2, Proc. Symp. Pure Math. 45:1-7 (1986).
2. 3, J. Funct. Anal. 9:296-305 (1972).
3. T. KATO, Quasi-linear equations of evolution, with applications to partial differential equations, Lecture Notes in Mathematics, 448:25-70 (1975).
4. J. WU, The inviscid limits for individual and statistical solutions of the Navier-Stokes equations, Ph.D. thesis, University of Chicago, 1996.
5. P. CONSTANTIN and J. WU, The inviscid limit for non-smooth vortivity, Indiana University Math. J. 45(1) (1996).
6. J. WU, The inviscid limit of the complex Ginzburg-Landau equation, J. Diff. Equations, 142(2):413-433 (1998).
7. J. BONA and J. WU, Zero dissipation limit for nonlinear waves, Preprint, 1999.
8. V. I. ARNOLD, Sur la geometrie differentielle des groupes de Lie de dimension infinie et ses applications a l'hydrodynamique des fluides parfaits, Ann. Inst. Fourier, Grenoble, 16(1):319-361 (1966).
9. J. E. MARSDEN, Lectures on Mechanics, Lond. Math. Soc. Lect. Note, Ser. 174, Cambridge University Press, Cambridge, 1992.
10. S. FRIEDLANDER and M. VISHIK, Lax pair formulation for the Euler equation, Phys. Lett. A 148(6-7):313-319 (1990).
11. M. VISHIK and S. FRIEDLANDER, An inverse scattering treatment for the flow of an ideal fluid in two dimensions, Nonlinearity 6(2):231-249 (1993).
12. Y. LI, A Lax pair for the 2D Euler equation, Submitted to Journal of Mathematical Physics, 2000.
13. Y. LI, On 2D Euler equations. Part II. Lax pairs and homoclinic structures, Comm. Appl. Nonl. Analysis 10(1):1-43 (2003).
14. S. CHILDRESS, Personal communication, 2000.
15. Y. LI, Bäcklund-Darboux transformations and Melnikov analysis for Davey-Stewartson II equations, J. Nonlinear Sci. 10(1): 103-131 (2000).
16. V. B. MATVEEV and M. A. SALLE, Darboux Transformations and Solitons, Vol. 4, Springer Series in Nonlinear Dynamics, 1991.
17. T. BEALE, T. KATO, and A. MAJDA, Remarks on the breakdown of smooth solutions for the 3-D Euler equations, Commun Math. Phys. 94(1):61-66 (1984).
18. Y. LI and R. SHVIDKOY, Isospectral theory of euler equations, submitted, 2002.
19. D. SERRE, Les invariants du premier ordre de l'equation d'Euler en dimension trois, Physica D 13:105-136 (1984).
20. D. BENNEY, Long waves, in Nonlinear Wave Motion, Lectures in Applied Mathematics, Vol. 15 (A. C. Newell, Ed.), pp. 49-60, 1974.
21. R. BEALS and R. R. COIFMAN, Linear spectral problems, non-linear equations and the ∂̄-method, Inverse Problems, 5:87-130 (1989).