Painleve analysis and exact solutions for the modified Korteweg–de Vries equation with polynomial source

Abstract

The modified Korteweg–de Vries equation with polynomial source is considered. Using the Painleve test we show that the generalized Korteweg–de Vries equation is not integrable by the inverse scattering transform. However there are some expansions of solution in the Laurent series and some exact solutions can exist. Some traveling wave solutions of the modified Korteweg–de Vries equation with polynomial source are found.