Solution of the Davey-Stewartson equation using homotopy analysis method (Q2815483)

This paper employs the homotopy analysis method (HAM) to solve the following Davey-Stewartson (DS) equation NEWLINE\[NEWLINE \begin{aligned} & iq_t+\frac{1}{2}\sigma^2(q_{xx}+\sigma^2q_{yy})+\lambda|q|^2q-\phi_xq=0,\\ & \phi_{xx}-\sigma^2\phi_{yy}-2\lambda(|q|^2)_x=0. \end{aligned}NEWLINE\]NEWLINE In order to show the accuracy of the method, the authors compare the results obtained by HAM to exact solutions and the homotopy perturbation method. Their comparisons indicate that the agreement between HAM solutions and exact solutions is very good in terms of accuracy.