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Zbl 0599.76028
Morrison, P.J.; Meiss, J.D.; Cary, J.R.
Scattering of regularized-long-wave solitary waves. (English)
[J] Physica D 11, 324-336 (1984). ISSN 0167-2789

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.

MSC 2000:: *76B25 Solitary waves, etc. (inviscid fluids)
35Q99 PDE of mathematical physics and other areas
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

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Zentralblatt MATH Berlin [Germany]