Perturbations on the K-dV Solitons —An Approach Based on the Multiple Time Scale Expansion—

Effects of perturbations on the soliton solutions of the K-dV equation are investigated. A system of equations which governs the slow modulation of the soliton solution is derived systematically from the non-secular conditions of the multiple time scale expansion. An equation which governs the time evolution of the non-soliton part is also obtained from the first order of the expansion. The results are applied to one soliton and two soliton problems. In addition, contributions of the non-soliton part to the modified conservation laws are investigated briefly.