APPLICATION OF THE partial derivative-DRESSING METHOD TO A (2+1)-DIMENSIONAL EQUATION

摘要

A remarkable method for investigating solutions of nonlinear soliton equation is the partial derivative-dressing method. Although there are other methods that can also be used for that aim, the partial derivative-dressing method is the most transparent and leads directly to the final results. The (2 + 1)-dimensional Sawada-Kotera equation is studied by analyzing the eigenfunction and the Green's function of its Lax representation as well as by the inverse spectral transformation, yielding a new partial derivative problem. The solution is constructed based on solving the partial derivative-problem by choosing a proper spectral transformation. Furthermore, once the time evolution of the spectral data is determined, we are able to completely obtain a formal solution of the Sawada-Kotera equation.