Morrison, P. J.; Meiss, J. D.; Cary, J. R. Scattering of regularized-long-wave solitary waves. (English) Zbl 0599.76028 Physica D 11, 324-336 (1984). The Lagrangian density for the regularized-long-wave equation (also known as the BBM equation) is presented. Using the trial function technique, ordinary differential equations that describe the time dependence of the position of the peaks, amplitudes, and widths for the collision of two solitary waves are obtained. These equations are analyzed in the Born and equal-width approximations and compared with numerical results obtained by direct integration utilizing the split-step fast Fourier-transform method. The computations show that collisions are inelastic and that production of solitary waves may occur. Cited in 60 Documents MSC: 76B25 Solitary waves for incompressible inviscid fluids 35Q99 Partial differential equations of mathematical physics and other areas of application 76M99 Basic methods in fluid mechanics 70Sxx Classical field theories Keywords:Lagrangian density for the regularized-long-wave equation; BBM equation; trial function technique; position of the peaks; collision of two solitary waves; equal-width approximations; numerical results; direct integration; split-step fast Fourier-transform method PDFBibTeX XMLCite \textit{P. J. Morrison} et al., Physica D 11, 324--336 (1984; Zbl 0599.76028) Full Text: DOI References: [1] Peregrine, D. H., J. Fluid Mech., 25, 321 (1966) [2] Meiss, J. D.; Horton, W., Phys. Fluids, 25, 1838 (1982) [3] Benjamin, T.; Bona, J.; Mahoney, J., Phil. Trans. R. Soc. London, A272, 47 (1972) [4] Kruskal, M. D., (Moser, J., Dynamical Systems, Theory and Applications (1976), Springer: Springer Berlin) [5] Bona, J. L.; Pritchard, W. G.; Scott, L. R., Phys. Fluids, 23, 438 (1980) [6] Olver, P. J., Math. Proc. Camb. Phil. Soc., 85, 143 (1979) [7] Tsujishia, T., Conservative Laws of the BBM Equation (1979), preprint [8] Hill, E. L., Rev. Mod. Phys., 23, 253 (1951) [9] Courant, R.; Hilbert, D., (Methods of Mathematical Physics, vol. I (1953), Wiley: Wiley New York), chap. IV · Zbl 0729.00007 [10] Tappert, F., Lect. Appl. Math., 15, 215 (1974) [11] Makino, M.; Kamimura, T.; Taniuti, T., J. Phys. Soc. Jap., 50, 980 (1981), Dr. T. Kamimura has generously provided us with his program. This algorithm was also used in the 2-D case by [12] Eilbeck, J. C.; McGuire, G. R., J. Comp. Phys., 23, 63 (1977) [13] Santarelli, A. R., Nuovo Cimento, 46, 179 (1978) [14] Courtenay Lewis, J.; Tjon, J. A., Phys. Lett., 73A, 275 (1979) 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.