Numerical Solution Of The Perturbed KdV Equation

In this paper, we investigate the initial value problem of the perturbed KdV equation:The approximate solution are obtained via the method of multiple scales corresponding to two kinds of perturbation: R{u) = δ(εt)u and R(u) = -Δ(εt)u_xxx. Then for the perturbed KdV equation :u_t +6uu_x +u_xxx = εR(u), (ε > 0)under the condition of that the initial data u₀(x)∈C^∞(-∞,+∞) decays exponentially as | x |→+∞ , energy equalities are constructed for the perturbed solitary wave solutions corresponding to two kinds of perturbations. Priori estimates of the bound of the solutions are obtained via the method of energy:(1) if R(u) = δ(εt)u, δ(s)∈C[0,+∞) and δ(0)=0, the solutions are...