In Section 2, Petrov-Galerkin method is used to derive a numerical method for the CKdV equation; a coupled nonlinear pentadigonal system is obtained.
To derive numerical method for the CKdV system, we consider the initial boundary value problem
and the CKdV system (1), we obtain the local truncation error (TTE) for the proposed scheme
A modified Petrov-Galerkin method for solving the CKdV system (1) can be achieved by using the product approximation technique, where we used special approximation to the nonlinear terms in the differential system.
We have tested other values of a; in all cases we have found that the interaction is inelastic and this in agreement with , which they claim the CKdV equation, is integrable only for a = 1/2.
In this work, we have derived two numerical schemes for solving the Hirota-Satsuma CKdV system.