Propagation of sech2-type solitary waves in hierarchical KdV-type systems

Authors:
Lauri Ilison;Andrus Salupere
Affiliations:
Centre for Nonlinear Studies, Institute of Cybernetics at Tallinn University of Technology, Akadeemia tee 21, 12618 Tallinn, Estonia and Department of Mechanics, Tallinn University of Technology, ...;Centre for Nonlinear Studies, Institute of Cybernetics at Tallinn University of Technology, Akadeemia tee 21, 12618 Tallinn, Estonia and Department of Mechanics, Tallinn University of Technology, ...
Venue:
Mathematics and Computers in Simulation
Year:
2009

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Abstract

A hierarchical Korteweg-de Vries-type evolution equation is applied for modelling wave propagation in dilatant granular materials. The model equation is integrated numerically under sech^2-type initial conditions using the Fourier transform-based pseudospectral method. Numerical simulations are carried out over a wide range of material parameters (two dispersion parameters and one microstructure parameter) and amplitudes of the initial wave. The analysis of the time-space behaviour of solutions results in five solution types. Besides typical KdV-like solitonic structures, wave packets were detected for some domains of material parameters.