Exact solutions and invariants of motion for general types of regularized long wave equations

  • Authors:

  • S. Hamdi;W. H. Enright;W. E. Schiesser;J. J. Gottlieb

  • Affiliations:

  • Department of Computer Science, University of Toronto, 10 King's College Road, Toronto, Canada M5S 3G4;Department of Computer Science, University of Toronto, 10 King's College Road, Toronto, Canada M5S 3G4;Mathematics and Engineering, Lehigh University, Bethlehem, PA;Institute for Aerospace Studies, University of Toronto, 4925 Dufferin Street, Toronto, Canada M3H 5T6

  • Venue:
  • Mathematics and Computers in Simulation - Special issue: Wave phenomena in physics and engineering: New models, algorithms, and appications
  • Year:
  • 2004

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Abstract

New exact solitary wave solutions are derived for general types of the regularized long wave (RLW) equation and its simpler alternative, the generalized equal width wave (EW) equation, which are evolutionary partial differential equations for the simulation of one-dimensional wave propagation in nonlinear media with dispersion processes. New exact solitary wave solutions are also derived for the generalized EW-Burgers equation, which models the propagation of nonlinear and dispersive waves with certain dissipative effects. The analytical solutions for these model equations are obtained for any order of the nonlinear terms and for any given value of the coefficients of the nonlinear, dispersive and dissipative terms. Analytical expressions for three invariants of motion for solitary wave solutions of the generalized EW equation are also devised.