Identification of solitary-wave solutions as an inverse problem: Application to shapes with oscillatory tails

Authors:
Christo I. Christov;Tchavdar T. Marinov;Rossitza S. Marinova
Affiliations:
Department of Mathematics, University of Louisiana at Lafayette, Lafayette, LA 70504-1010, USA;Department of Natural Sciences, Southern University at New Orleans, 6801 Press Drive, New Orleans, LA 70126, USA;Department of Mathematical & Computing Sciences, Concordia University College of Alberta, Edmonton, AB, T5B 4E4, Canada
Venue:
Mathematics and Computers in Simulation
Year:
2009

Citing 3
Cited 0

Homoclinic orbits in reversible systems and their applications in mechanics, fluids and optics

Proceedings of the workshop on Time-reversal symmetry in dynamical systems
Interacting localized waves for the regularized long wave equation via a Galerkin spectral method

Mathematics and Computers in Simulation - Special issue: Nonlinear waves: Computation and theory III
Numerical Recipes 3rd Edition: The Art of Scientific Computing

Numerical Recipes 3rd Edition: The Art of Scientific Computing

Quantified Score

Hi-index	0.00

Visualization

Abstract

The propagation of stationary solitary waves on an infinite elastic rod on elastic foundation equation is considered. The asymptotic boundary conditions admit the trivial solution along with the solution of type of solitary wave, which is a bifurcation problem. The bifurcation is treated by prescribing the solution in the origin and introducing an unknown coefficient in the equation. Making use of the method of variational imbedding, the inverse problem for the coefficient identification is reformulated as a higher-order boundary value problem. The latter is solved by means of an iterative difference scheme, which is thoroughly validated. Solitary waves with oscillatory tails are obtained for different values of tension and linear restoring force. Special attention is devoted to the case with negative tension, when the solutions have oscillatory tails.