ON EXISTENCE OF PERIODIC SOLUTIONS OF THE KDV TYPE EQUATION

Year 2011, Volume: 01 Issue: 2, 167 - 172, 01.12.2011

Talaibek M. Imanaliev

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

References

• [1] Imanaliev, M., Pankov, P. S. and Imanaliev,T. M., (1995), On The Theory of Partial Differential Equations of KDV type, 342(1), 17-19.
• [2] Imanaliev, M., Pankov, P. S. and Imanaliev,T. M., (1995), On The Theory of Nonlinear Partial Wave Equations, Doklady Academii Nauk, 343(5), 596-598.
• [3] Imanaliev,T. M., (1998), On the Theory of Multiperiodic Solutions of Nonlinear Partial Equations of KDV Type, Research on Integro-Differential Equations. - Bishkek: Ilim, 27, 26-30.
• [4] Imanaliev,T. M., (1998), On Periodic Solutions of KDV Type Equation, Research on Integro-Differential Equations. - Bishkek: Ilim, 27, 31-37.