Raslan, K. R. A computational method for the regularized long wave (RLW) equation. (English) Zbl 1082.65582 Appl. Math. Comput. 167, No. 2, 1101-1118 (2005). Summary: A numerical solution of the regularized long wave equation, based on collocation method using cubic B-spline finite elements is used to simulate the migration and interaction of solitary waves. Interaction of solitary waves with different amplitudes are shown. The three invariants of the motion are evaluated to determine the conservation properties of the system. The temporal evaluation of a Maxwellian initial pulse is then studied, and then we prove that the number of solitons which are generated from Maxwellian initial condition are determined. Cited in 66 Documents MSC: 65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs 35L75 Higher-order nonlinear hyperbolic equations 65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs 37K40 Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems 35Q51 Soliton equations Keywords:RLW; Finite element methods; Splines; Solitons; numerical examples; regularized long wave equation; collocation method; solitary waves PDFBibTeX XMLCite \textit{K. R. Raslan}, Appl. Math. Comput. 167, No. 2, 1101--1118 (2005; Zbl 1082.65582) Full Text: DOI References: [1] Peregrine, D. H., Calculations of the development of an undular bore, J. Fluid Mech., 25, 321-330 (1966) [2] Abdulloev, Kh. O.; Bogalubsky, H.; Markhankov, V. G., One more example of inelastic soliton interaction, Phys. Lett., 56A, 427-428 (1976) [3] Elibeck, J. C.; McGuire, G. R., Numerical study of the RLW equation II: Interaction of solitary waves, J. Comput. Phys., 23, 63-73 (1977) · Zbl 0361.65100 [4] Bona, J. L.; Pritchard, W. G.; Scott, L. R., Numerical scheme for a model of nonlinear dispersive waves, J. Comput. Phys, 60, 167-176 (1985) · Zbl 0578.65120 [5] Alexander, M. E.; Morris, J. H., Galerkin method for some model equations for nonlinear dispersive waves, J. Comput. Phys., 30, 428-451 (1979) · Zbl 0407.76014 [6] Wahlbin, L., Numer. Math., 289 (1975) [7] gardner, L. R.T.; Gardner, G. A., Solitary waves of RLW equation, J. Comput. Phys., 91, 441-459 (1991) · Zbl 0717.65072 [8] Jain, P. C.; Shankar, R.; Singh, T. V., Numerical solutions of RLW equation, Commun. Numer. Meth. Eng., 9, 587-594 (1993) [9] Gardner, L. R.T.; Gardner, G. A.; Dogan, A., A least-squares FE scheme for the RLW equation, Commun. Numer. Meth. Eng., 12, 795-804 (1996) · Zbl 0867.76040 [10] Saki, S. I., Solitary waves of the splitted RLW equation, Comput. Phys. Commun., 138, 80-91 (2001) · Zbl 0984.65103 [11] K.R. Raslan, Numerical methods for partial differential equations, Ph.D. Thesis, Al-Azhar University, Cairo, 1999.; K.R. Raslan, Numerical methods for partial differential equations, Ph.D. Thesis, Al-Azhar University, Cairo, 1999. [12] A.K. Khalifa, Theory and applications of the collocation method with spline for ordinary and partial differential equations, Ph.D. Thesis, Heriot-Watt University, 1979.; A.K. Khalifa, Theory and applications of the collocation method with spline for ordinary and partial differential equations, Ph.D. Thesis, Heriot-Watt University, 1979. [13] Olver, P. J., Euler operators and conservation laws of the BBM equation, Math. Proc. Combradge Philos. Soc., 85, 143-159 (1979) · Zbl 0387.35050 [14] Santarelli, A. R., Numerical analysis of the regularised long wave equation, Nuovo Cim, 39, 94-102 (1981) [15] Courtenay Lewis, J.; Tjon, J. A., Resonant production of solitons in the RLW equation, Phys. Lett., 73A, 275-279 (1979) [16] Raslan, K. R., A computational methods for the equal width equation, Int. J. Comput. Math., 81, l, 63-72 (2004) · Zbl 1047.65086 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.