On the second-order approximate symmetry classification and optimal systems of subalgebras for a forced Korteweg-de Vries equation

We investigate a forced Korteweg-de Vries (fKdV) equation, u,t+cu,x+αuu,x+βu,xxx=βF(t), which arises in the modelling of tsunami generation by submarine landslides. Approximate symmetries are found for the fKdV equation using the method as proposed by Fushchich and Shtelen [6]. Symmetries are found to second order in the perturbation parameter using the MAPLE symmetry package ASP [11], an add-on to the symmetry package DESOLVII [18]. ASP also allows particular forms of the arbitrary function F(t) to be found which extend the symmetry algebra and hence a full approximate symmetry classification of the fKdV equation is obtained. Optimal systems of one-dimensional subalgebras are also determined. Corresponding approximate invariant solutions to the fKdV equation are then constructed for particular F(t) using DESOLVII routines.

Communications in Nonlinear Science and Numerical Simulation

Communications in Nonlinear Science and Numerical Simulation

18

1007-5704

N/A

9

19