Abstract:

To find exact soliton-like solution of the Calogero-Degasperis-Fokas (CDF) equation the direct perturbation method is used. We found that the continued fraction corresponding to the perturbation series is cut off and the remaining finite fraction gives the exact solution of the CDF equation. It is shown that if continued fraction is cut off then the corresponding series is geometric. The criterion is proposed under which a continuous fraction is converted to a finite fraction.

Keywords: exact solitary-wave solutions, perturbation method, continued fraction