A study of higher order terms in shallow water waves via modified PLK method

In this work, by utilizing the modified PLK (Poincare-Lighthill-Kou) method, we studied the propagation of weakly nonlinear waves in a shallow water theory and obtained the Korteweg-deVries (KdV) and the linearized KdV equations with non-homogeneous term as the governing equations of various order terms in the perturbation expansion. The result obtained here is exactly the same with that of Kodama and Taniuti [6], who employed the so-called "re-normalization method". Seeking a progressive wave solution to these evolution equations we obtained the speed correction terms so as to remove some possible secularities. The result obtained here is consistent with the results of Demiray [12], wherein the modified reductive perturbation method had been utilized.