×

Conservative scheme for a model of nonlinear dispersive waves and its solitary waves induced by boundary motion. (English) Zbl 0739.76037

The authors have given a conservative difference scheme for a model of nonlinear dispersive waves. Convergence and stability of the scheme are proved. Using the scheme, the authors have explored numerically the relationship between the boundary data and the amplitudes and number of solitary waves it produces.
Reviewer: J.Prakash (Bombay)

MSC:

76M20 Finite difference methods applied to problems in fluid mechanics
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
76B25 Solitary waves for incompressible inviscid fluids
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Benjamin, T. B.; Bona, J. L.; Mahony, J. J.: Philos. trans. Roy. soc. London A. 272, 47 (1972)
[2] Bona, J. L.; Pritchard, W. G.; Scott, L. R.: Philos. trans. Roy. soc. London A. 302, 457 (1981)
[3] Chu, C. K.; Xiang, L. W.; Baransky, Y.: Commun. pure appl. Math.. 36, 495 (1983)
[4] Bona, J. L.; Pritchard, W. G.; Scott, L. R.: J. comput. Phys.. 60, 167 (1985)
[5] Guo, B.; Chang, Q.: Mon. J. Sci.. 28, 310 (1983)
[6] Filbeck, J. C.; Mcguire, G. R.: J. compzet. Phys.. 19, 43 (1975)
[7] Eilbeck, J. C.; Mcguire, G. R.: J. comput. Phys.. 23, 63 (1977)
[8] Alexander, M. E.; Morris, J. L.: J. comput. Phys.. 30, 428 (1979)
[9] Menikoff, A.: Commun. pure appl. Math.. 25, 407 (1972)
[10] Fornberg, B.; Whitham, G. B.: Philos. trans. Roy. soc. London A. 289, 373 (1978) · Zbl 0384.65049
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.