A Numerical Simulation of Solitary-Wave Solutions of the Generalized Regularized Long-Wave Equation

We consider solitary-wave solutions of the generalized regularized long-wave (RLW) equation u"t+u"[email protected](u^p)"[email protected]"x"x"t=0. In this paper by considering the decomposition scheme, we first obtain the exact solitary-wave solutions of the generalized RLW equation for the initial condition without using any classical transformations and then its numerical solutions are constructed without using any discretization technique. The numerical solutions are compared with the known analytical solutions. Its remarkable accuracy is finally demonstrated in the study of some values p>=2 of the generalized RLW equation.

[1]  J. Bona,et al.  Model equations for long waves in nonlinear dispersive systems , 1972, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences.

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

[3]  Y. Cherruault,et al.  Decomposition methods: A new proof of convergence , 1993 .

[4]  Juan M. Restrepo,et al.  Stable and Unstable Solitary-Wave Solutions of the Generalized Regularized Long-Wave Equation , 2000, J. Nonlinear Sci..

[5]  C. S. Gardner,et al.  Korteweg-devries equation and generalizations. VI. methods for exact solution , 1974 .

[6]  M. C. Shen,et al.  Asymptotic Theory of Unsteady Three-Dimensional Waves in a Channel of Arbitrary Cross Section , 1969 .

[7]  A. Rèpaci,et al.  Nonlinear dynamical systems: On the accuracy of adomian's decomposition method , 1990 .

[8]  Y. Cherruault.  Convergence of Adomian's method , 1989 .

[9]  D. Kaya,et al.  A New Approach to Solve a Nonlinear Wave Equation , 1998 .

[10]  L. R. Scott,et al.  A Comparison of Solutions of Two Model Equations for Long Waves. , 1983 .

[11]  D. Kaya.  On the solution of a korteweg-de vries like equation by the decomposition method , 1999, Int. J. Comput. Math..

[12]  Abdul-Majid Wazwaz,et al.  A new algorithm for calculating adomian polynomials for nonlinear operators , 2000, Appl. Math. Comput..

[13]  George Adomian,et al.  Solving Frontier Problems of Physics: The Decomposition Method , 1993 .

[14]  Dogan Kaya,et al.  An application of the decomposition method for second order wave equations , 2000, Int. J. Comput. Math..

[15]  D. Korteweg,et al.  XLI. On the change of form of long waves advancing in a rectangular canal, and on a new type of long stationary waves , 1895 .

[16]  G. Adomian.  A review of the decomposition method in applied mathematics , 1988 .

[17]  D. Peregrine.  Long waves on a beach , 1967, Journal of Fluid Mechanics.

[18]  C. S. Gardner,et al.  The Korteweg-de Vries equation as a Hamiltonian System , 1971 .