## ON EXISTENCE OF PERIODIC SOLUTIONS OF THE KDV TYPE EQUATION

## ON EXISTENCE OF PERIODIC SOLUTIONS OF THE KDV TYPE EQUATION

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*Talaibek M. Imanaliev *

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## Abstract

We prove the existence of the periodic solutions of the KDV type of equation with respect to time variable with periodic external force. Using the integral substitution we reduce the original equation to the integral equation. The existence of the unique solution of the equation is proved by the fixed point theorem. Thus we show that the solitons are periodic in time as well as in space dimension.

## Keywords

Periodic solution, KDV type equation, nonlinear integral equation, contractive operator.