New framework for studying the stability of genus-1 and genus-2 KP patterns

European Journal of Mechanics, B/Fluids

Volumn 18, Issue 3, 1999, Pages 493-500

  Bridges, Thomas J ^a  

^a UNIVERSITY OF SURREY   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EQUATIONS OF MOTION; FLOW OF WATER; FLOW PATTERNS; FUNCTIONS; INTEGRATION; MATHEMATICAL MODELS; SURFACE WAVES;

KADOMTSEV-PETVIASHVILI (KP) EQUATION; RIEMANN THETA FUNCTIONS;

WATER WAVES;

EID: 0033131795     PISSN: 09977546     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0997-7546(99)80044-2     Document Type: Article

References (14)

1. de Bouard, A., Saut, J. C., 1997 Symmetries and decay of the generalized Kadomtsev-Petviashvili solitary waves, SIAM J. Math. Anal. 28, 1064-1085.
2. Bridges, T. J., 1995 Multi-symplectic structures, boussinesq equations and periodic travelling waves, Proceedings of the IUTAM Symposium on Nonlinear Waves in Fluids, (Eds. A. Mielke & K. Kirchgässner), World Scientific: Singapore.
3. Bridges, T. J., 1996 Periodic patterns, linear instability, symplectic structure and mean-flow dynamics for three-dimensional surface waves, Phil. Trans. Roy. Soc. Lond. A354, 533-74.
4. Bridges, T. J., 1997a Multi-symplectic structures and wave propagation, Math. Proc. Camb. Phil. Soc. 121, 147-190.
5. Bridges, T. J., 1997b A geometric formulation of the conservation of wave action and its implications for signature and the classification of instabilities, Proc. Roy. Soc. Lond. A453, 1365-1395.
6. Bridges, T. J., 1998 Toral-equivariant partial differential equations and quasiperiodic patterns, Nonlinearity 11, 467-500.
7. Dubrovin, B. A., 1981 Theta functions and nonlinear equations, Russ. Math. Surveys 36, 11-92.
8. Dubrovin, B. A., Flickinger, R., Segur, H., 1997 Three-phase solutions of the Kadomtsev-Petviashvili equation, Stud. Appl. Math. 99, 137-203.
9. Hammack, J., McCallister, D., Scheffner, N., Segur, H., 1995 Two-dimensional periodic waves in shallow water. Part 2. Asymmetric waves, J. Fluid Mech. 285, 95-122.
10. Kadomtsev, B. B., Petviashvili, V. I., 1970 On the stability of solitary waves in weakly dispersive media, Sov. Phys. Dokl. 15, 539-541.
11. Infeld, I., Rowlands, G., 1990 Nonlinear Waves, Solitons and Chaos, Cambridge University Press.
12. Segur, H., Finkel, A., 1985 An analytical model of periodic waves in shallow water, Stud. Appl. Math. 73, 183-220.
13. Whitham, G. B., 1974 Linear and Nonlinear Waves, Wiley-Interscience Publishers: New York.
14. Wang, X. P., Ablowitz, M. J., Segur, H., 1994 Wave collapse and instability of solitary waves of a generalized Kadomtsev-Petviashvili equation, PhysicaD 78, 241-265.