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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
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[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
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