Solitary waves for Korteweg–de Vries equation with small delay

This paper deals with the existence of solitary waves for Korteweg–de Vries equation with time delay. Based upon the inertial manifold theory and differential manifold geometric theory, the existence of solitary wave solution is proved when the delay is small enough. Up to now, studies on solitary wave for such delay differential equation are not available, so the results of this paper are new.