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Solitary waves of the equal width wave equation. (English) Zbl 0759.65086
In a recent paper of the authors [ibid. 91, No. 2, 441-459 (1990; Zbl 0717.65072)] a Galerkin method with cubic \(B\)-spline finite elements was proposed to obtain accurate and efficient numerical solutions to the regularized long wave (RLW) equation. Here, the same method is applied to the equal width equation and to simulate the migration and interaction of solitary waves and evolution of a Maxwellian initial condition.
For small \(\delta\) \((U_ t+UU_ x-\delta U_{xxt}=0)\) only positive waves are formed and the behaviour mimics that of the KdV and RLW equations. For larger values of \(\delta\) both positive and negative solitary waves are generated.
Reviewer: L.G.Vulkov (Russe)

65Z05 Applications to the sciences
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
35Q53 KdV equations (Korteweg-de Vries equations)
35L75 Higher-order nonlinear hyperbolic equations
Full Text: DOI
[1] Peregrine, D.H., J. fluid mech., 25, 321, (1966)
[2] Abdulloev, Kh.O.; Bogolubsky, H.; Markhankov, V.G., Phys. lett. A, 56, 427, (1976)
[3] Morrison, P.J.; Meiss, J.D.; Cary, J.R., Physica D, 11, 324, (1984)
[4] Santarelli, A.R., Nuovo cimento B, 46, 179, (1978)
[5] Lewis, J.C.; Tjon, J.A., Phys. lett. A, 73, 275, (1979)
[6] Eilbeck, J.C.; McGuire, G.R., J. comput. phys., 23, 63, (1977)
[7] Bona, J.L.; Pritchard, W.G.; Scott, L.R., J. comput. phys., 60, 167, (1985)
[8] Alexander, M.E.; Morris, J.H., J. comput. phys., 30, 428, (1979)
[9] Wahlbin, L., Numer. math., 23, 289, (1975)
[10] Gardner, L.R.T.; Gardner, G.A., J. comput. phys., 91, 441, (1990)
[11] Olver, P.J., (), 143
[12] Sanz-Serna, J.M.; Christie, I., J. comput. phys., 39, 94, (1981)
[13] Berezin, Yu.A.; Karpman, V.I., Sov. phys. JEPT, 24, 1049, (1967)
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