Fourier splitting and dissipation of nonlinear dispersive waves

Royal Society of Edinburgh - Proceedings A

Volumn 129, Issue 3, 1999, Pages 477-502

  Bona, J L ^a   Demengel, F ^b   Promislow, K ^c  

^a UNIVERSITY OF TEXAS AT AUSTIN   (United States)

^b UNIVERSITÉ DE CERGY PONTOISE   (France)

^c SIMON FRASER UNIVERSITY   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 22644448659     PISSN: 03082105     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0308210500021478     Document Type: Article

References (26)

1. C. J. Amick, J. L. Bona and M. E. Schonbek. Decay of solutions of some nonlinear wave equations. J. Diffl Eqns 81 (1989), 1-49.
2. T. B. Benjamin. Lectures on nonlinear wave motion. In Nonlinear wave motion (ed. A. C. Newell), pp. 3-47. Lectures in Applied Mathematics, vol. 15 (Providence, RI: AMS, 1974).
3. P. Biler. Asymptotic behavior in time of solutions to some equations generalizing the Korteweg-de Vries equation. Bull. Polish Acad. Sci. 32 (1984), 275-282.
4. J. L. Bona. On solitary waves and their role in the evolution of long waves. Applications of nonlinear analysis in the physical sciences (ed. H. Amann, N. Bazley and K. Kirchgassner), pp. 183-205 (London: Pitman, 1981).
5. J. L. Bona, V. Dougalis, O. Karakashian and W. McKinney. Computations of blow-up and decay for periodic solutions of the generalized Korteweg-de Vries-Burgers equation. Appl Numer. Math. 10 (1992), 335-355.
6. J. L. Bona and L. Luo. More results on the decay of solutions to nonlinear, dispersive, wave equations. Discrete Contin. Dynam. Systems 1 (1995), 151-193.
7. J. L. Bona, K. Promislow and C. E. Wayne. On the asymptotic behavior of solutions to nonlinear, dispersive, dissipative wave equations. J. Math. Computers Simulation 37 (1994), 265-277.
8. J. L. Bona, K. Promislow and C. B. Wayne. Higher-order asymptotics of decaying solutions of some nonlinear dispersive, dissipative wave equations. Nonlinearity 8 (1995), 1179-1206.
9. J. L. Bona, W. G. Pritchard and L. R. Scott. An evaluation of a model equation for water waves Phil. Trans. R. Soc. Lond. A 302 (1981), 457-510.
10. J. Bricmont, A. Kupiainen and G. Lin. Renormalization group and asymptotics of solutions of nonlinear parabolic equations. Commun. Pure Appl. Math. 47 (1994), 893-922.
11. D. B. Dix. The dissipation of nonlinear dispersive waves: the case of asymptotically weak nonlinearity. Commun. PDE 17 (1992), 1665-1693.
12. C. S. Gardner, J. M. Greene, M. D. Kruskal and R. M. Miura. A method for solving the Korteweg-de Vries equation. Phys. Rev. Lett. 19 (1967), 1095-1097.
13. C. S. Gardner, J. M. Greene, M. D. Kruskal and R. M. Miura. Korteweg-de Vries equation and generalizations. VI. Methods for exact solution. Commun. Pure Appl. Math 27 (1974), 97-133.
14. J. L. Hammack. A note on tsunamis: their generation and propagation in an ocean of uniform depth. J. Fluid Mech. 60 (1974), 769-799.
15. J. L. Hammack and H. Segur. The Korteweg-de Vries equation and water waves. Part 2. Comparison with experiments. J. Fluid Mech. 65 (1974), 289-314.
16. T. Kakutani and K. Matsuuchi. Effect of viscosity on long gravity waves. J. Phys. Soc. Jpn 39 (1975), 237-246.
17. T. Kato. On the Cauchy problem for the (generalized) Korteweg-de Vries equation. In Stud. Appl. Math. (Suppl.) 8 (1983), 93-128 (New York: Academic Press).
18. A. Mielke. Locally invariant manifolds for quasilinear parabolic equations. Rocky Mountain J. Math. 21 (1991), 708-714.
19. J. J. Mahony and W. G. Pritchard. Wave reflexion from beaches. J. Fluid Mech. 101 (1980), 809-832.
20. P. Naumkin and I. Shishmarev. Nonlinear nonlocal equations in the theory of waves. Translations of Mathematics Monographs, vol. 133 (Providence, RI: AMS, 1994).
21. E. Ott and R. N. Sudan. Phys. Fluids 12 (1969), 2388.
22. E. Schechter. Well-behaved evolutions and Trotter product formulas. PhD thesis, University of Chicago, 1978.
23. m spaces. Commun. PDE 20 (1995), 103-117.
24. M. E. Schonbek. Decay of solutions to parabolic conservation laws. Commun. PDE 7 (1980), 449-473.
25. M. E. Schonbek and S. Rajopadhye. Asymptotic behavior of solutions to the Korteweg-de Vries-Burgers system. Ann. Inst. H. Poincaré Analysis NonLinéaire 12 (1995), 425-457.
26. C. E. Wayne. Invariant manifolds for parabolic partial differential equations on unbounded domains. Arch. Ration. Mech. Analysis 138 (1997), 279-306.