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

- [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.

- [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.

Primary Language | English |
---|---|

Journal Section | Research Article |

Authors | |

Publication Date | December 1, 2011 |

Published in Issue | Year 2011, Volume 01, Issue 2 |

Bibtex | @ { twmsjaem761792, journal = {TWMS Journal of Applied and Engineering Mathematics}, issn = {2146-1147}, eissn = {2587-1013}, address = {Işık University ŞİLE KAMPÜSÜ Meşrutiyet Mahallesi, Üniversite Sokak No:2 Şile / İstanbul}, publisher = {Turkic World Mathematical Society}, year = {2011}, volume = {01}, number = {2}, pages = {167 - 172}, title = {ON EXISTENCE OF PERIODIC SOLUTIONS OF THE KDV TYPE EQUATION}, key = {cite}, author = {Imanaliev, Talaibek M.} } |