TY - JOUR
T1 - Interacting localized waves for the regularized long wave equation via a Galerkin spectral method
AU - Christou, M. A.
AU - Christov, C. I.
PY - 2005/6/24
Y1 - 2005/6/24
N2 - We develop a Fourier-Galerkin spectral technique for computing the solutions of type of interacting localized waves. To this end, a special complete orthonormal system of functions in L2(-∞,∞) is used and a time-stepping algorithm implementing the spectral method is developed. The rate of convergence of the coefficients is shown to be exponential. We consider the regularized long wave equation (RLWE) which is not fully integrable. We demonstrate the stability of the algorithm and find numerically the threshold for the existence of such interactions. We also calculate the phase shifts of the interactions and compare them to the finite-difference solution.
AB - We develop a Fourier-Galerkin spectral technique for computing the solutions of type of interacting localized waves. To this end, a special complete orthonormal system of functions in L2(-∞,∞) is used and a time-stepping algorithm implementing the spectral method is developed. The rate of convergence of the coefficients is shown to be exponential. We consider the regularized long wave equation (RLWE) which is not fully integrable. We demonstrate the stability of the algorithm and find numerically the threshold for the existence of such interactions. We also calculate the phase shifts of the interactions and compare them to the finite-difference solution.
KW - Galerkin spectral method
KW - Localized waves
KW - Regularized long wave equation
UR - http://www.scopus.com/inward/record.url?scp=19044375660&partnerID=8YFLogxK
U2 - 10.1016/j.matcom.2005.01.004
DO - 10.1016/j.matcom.2005.01.004
M3 - Article
AN - SCOPUS:19044375660
SN - 0378-4754
VL - 69
SP - 257
EP - 268
JO - Mathematics and Computers in Simulation
JF - Mathematics and Computers in Simulation
IS - 3-4
ER -