Solitonic Solutions for Homogeneous KdV Systems by Homotopy Analysis Method

Applications in physics are modeled by nonlinear systems. Very few nonlinear systems have closed form solutions, therefore, many researchers stress their goals to search numerical solutions. Homotopy analysis method HAM , first proposed by Liao 1 , is an elegant method which has proved its effectiveness and efficiency in solving many types of nonlinear equations 2, 3 . Liao in his book 4 proved that HAM is a generalization of some previously used techniques such as the d-expansion method, artificial small parameter method 5 , and Adomian decomposition method. Moreover, unlike previous analytic techniques, the HAM provides a convenient way to adjust and control the region and rate of convergence 6 . Recently, new interested applications of the homotopy analysis have been introduced by Abbasbandy and coauthors 7, 8 . Also, in 9 HAM is used to study the effects of thermocapillarity and thermal radiation on flow and heat transfer in a thin liquid film. In this work, we consider a two-component evolutionary system of a homogeneous KdV equations of third order type I and II given, respectively, by