Effect of a Localized Random Forcing Term on the Korteweg-De Vries Equation

Journal of Computational Analysis and Applications

Volumn 3, Issue 3, 2001, Pages 183-206

  Debussche, Arnaud ^a   Printems, Jacques ^b,c  

^a UNIVERSITÉ PARIS SACLAY   (France)

^b UNIVERSITÉ PARIS 13   (France)

^c UNIVERSITÉ PARIS EST CRÉTEIL   (France)

Author keywords

Korteweg de Vries equation; Least squares finite element method; Random waves; Solitons; Water waves

Indexed keywords

EID: 0013000861     PISSN: 15211398     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1011596026830     Document Type: Article

References (25)

1. T. R. Akylas, On the excitation of long nonlinear water waves by a moving pressure distribution, J. Fluid. Mech. 141, 455-466 (1984).
2. J. L. Bona and B.-Y. Zhang, The initial value problem for the forced Korteweg-de Vries equation, Proc. Roy. Soc. Edinburgh 126A, 571-598 (1996).
3. G. F. Carey and Y. Shen, Approximations of the KdV equation by least squares finite elements, Comput. Methods Appl. Mech. Engrg. 93, 1-11 (1991).
4. H. Y. Chang, Ch. Lien, S. Sukarto, S. Raychaudhury, J. Hill, E. K. Tsikis, and K. E. Lonngren, Propagation of ion-acoustic solitons in a non-quiescent plasma, Plasma Phys. Controlled Fusion 28, 675-681 (1986).
5. S. L. Cole, Transcient waves produced by flow past a bump, Wave motion 7, 579-587 (1985).
6. A. Debussche and A. de Bouard, On the stochastic Korteweg-de Vries equation, J. Funct. Anal. 154, 215-251 (1998).
7. A. Debussche, A. de Bouard, and Y. Tsutsumi, White noise driven stochastic Korteweg-de Vries equation, J. Funct. Anal. 169, 532-558 (1999).
8. A. Debussche and J. Printems, Numerical simulation of the stochastic Korteweg-de Vries equation, Physica D 134(2), 200-226 (1999).
9. R. Grimshaw, Resonant flow of a rotating fluid past an obstacle: the general case, Stud. Appl. Math. 83, 249-269 (1990).
10. R. Grimshaw, Resonant forcing of barotropic coastally trapped waves, J. Phys. Ocean. 17, 53-65 (1987).
11. R. Grimshaw, E. Pelinovsky, and X. Tian, Interaction of a solitary wave with an external force, Physica D 77, 405-433 (1994).
12. R. Grimshaw and N. Smyth, Resonant flow of a stratified fluid over topography, J. Fluid Mech. 169, 429-464 (1986).
13. R. Grimshaw and Z. Yi, Resonant generation of finite-amplitude waves by flow past topography on a beta-plane, Stud. Appl. Math. 88, 89-112 (1993).
14. R. Herman, The stochastic, damped Korteweg-de Vries equation, J. Phys. A: Math. Gen. 23, 1063-1084 (1990).
15. V. V. Konotop and L. Vasquez, Nonlinear Random Waves, World Scientific, Singapore, 1994.
16. S.-J. Lee, G. T. Yates, and T. Y. Wu, Experiments and analyses of upstream-advancing solitary waves generated by moving disturbances, J. Fluid. Mech. 199, 569-593 (1989).
17. W. K. Melville and K. R. Helfrich, Transcritical two-layer flow over topography, J. Fluid Mech. 178, 31-52 (1987).
18. H. Mitsudera and R. Grimshaw, Generation of mesoscale variability by resonant interaction between a baroclinic current and localized topography, J. Phys. Ocean. 21, 737-765 (1991).
19. A. Patoine and T. Warn, The interaction of long, quasi-stationary baroclinic waves with topography, J. Atmos. Sci. 39, 1018-1025 (1982).
20. 2(ℝ), J. Diff. Equations 153, 338-373 (1999).
21. M. Scalerandi, A. Romano, and C. A. Condat, Korteweg-de Vries solitons under additive stochastic perturbations, Phys. Rev. E 58, 4166-4173 (1998).
22. M. Wadati, Stochastic Korteweg-de Vries equation, J. Phys. Soc. Jpn 52, 2642-2648 (1983).
23. T. Warn and B. Brasnett, The amplification and capture of atmospheric solitons by topography: a theory of the onset of regional blocking, J. Atmos. Sci. 40, 28-38 (1983).
24. G. B. Whitham, Linear and Nonlinear Waves (Pure and Applied Mathematics), Wiley Interscience, New York, 1974.
25. T. Y. Wu, Generation of upstream advancing solitons by moving disturbances, J. Fluid Mech. 184, 75-99 (1987).