A computational method for the regularized long wave (RLW) equation

A numerical solution of the regularized long wave (RLW) 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.

[1]  L. R. Scott,et al.  Numerical schemes for a model for nonlinear dispersive waves , 1985 .

[2]  V. G. Makhankov,et al.  One more example of inelastic soliton interaction , 1976 .

[3]  M. E. Alexander,et al.  Galerkin methods applied to some model equations for non-linear dispersive waves , 1979 .

[4]  A. K. Khalifa,et al.  Theory and applications of the collocation method with splines for ordinary and partial differential equations , 1979 .

[5]  A. Santarelli,et al.  Numerical analysis of the regularized long-wave equation: Anelastic collision of solitary waves , 1978 .

[6]  Abdulkadir Dogan,et al.  A least‐squares finite element scheme for the RLW equation , 1996 .

[7]  S. Zaki,et al.  Solitary waves of the splitted RLW equation , 2001 .

[8]  P. Jain,et al.  Numerical solution of regularized long-wave equation , 1993 .

[9]  K. R. Raslan,et al.  A computational method for the equal width equation , 2004, Int. J. Comput. Math..

[10]  Peter J. Olver,et al.  Euler operators and conservation laws of the BBM equation , 1979, Mathematical Proceedings of the Cambridge Philosophical Society.

[11]  L. Gardner,et al.  Solitary waves of the regularized long-wave equation , 1990 .

[12]  D. Peregrine.  Calculations of the development of an undular bore , 1966, Journal of Fluid Mechanics.

[13]  J. A. Tjon,et al.  Resonant production of solitons in the RLW equation , 1979 .

[14]  G. R. McGuire,et al.  Numerical Study of the Regularized Long-Wave Equation. II: Interaction of Solitary Waves , 1977 .