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ON EXISTENCE OF PERIODIC SOLUTIONS OF THE KDV TYPE EQUATION

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

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

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.

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

Abstract

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.

Details

Primary Language English
Journal Section Research Article
Authors

Talaibek M. IMANALİEV This is me
Department of Applied Mathematics Kyrgyz National University, Bishkek, Kyrgyzstan

Publication Date December 1, 2011
Published in Issue Year 2011, Volume 01, Issue 2

Cite

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.} }