ON EXISTENCE OF PERIODIC SOLUTIONS OF THE KDV TYPE EQUATION

Volume: 01 Number: 2 December 1, 2011
  • Talaibek M. Imanaliev
TWMS Journal of Applied and Engineering Mathematics Cover
TWMS Journal of Applied and Engineering Mathematics
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ON EXISTENCE OF PERIODIC SOLUTIONS OF THE KDV TYPE EQUATION

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

References

  1. [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. [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. [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. [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

Subjects

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Journal Section

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Authors

Talaibek M. Imanaliev This is me

Publication Date

December 1, 2011

Submission Date

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Acceptance Date

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Published in Issue

Year 2011 Volume: 01 Number: 2

IZ

https://izlik.org/JA28CT33WH

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RIS / Bibtex
APA
Imanaliev, T. M. (2011). ON EXISTENCE OF PERIODIC SOLUTIONS OF THE KDV TYPE EQUATION. TWMS Journal of Applied and Engineering Mathematics, 01(2), 167-172. https://izlik.org/JA28CT33WH
AMA
1.Imanaliev TM. ON EXISTENCE OF PERIODIC SOLUTIONS OF THE KDV TYPE EQUATION. JAEM. 2011;01(2):167-172. https://izlik.org/JA28CT33WH
Chicago
Imanaliev, Talaibek M. 2011. “ON EXISTENCE OF PERIODIC SOLUTIONS OF THE KDV TYPE EQUATION”. TWMS Journal of Applied and Engineering Mathematics 01 (2): 167-72. https://izlik.org/JA28CT33WH.
EndNote
Imanaliev TM (December 1, 2011) ON EXISTENCE OF PERIODIC SOLUTIONS OF THE KDV TYPE EQUATION. TWMS Journal of Applied and Engineering Mathematics 01 2 167–172.
IEEE
[1]T. M. Imanaliev, “ON EXISTENCE OF PERIODIC SOLUTIONS OF THE KDV TYPE EQUATION”, JAEM, vol. 01, no. 2, pp. 167–172, Dec. 2011, [Online]. Available: https://izlik.org/JA28CT33WH
ISNAD
Imanaliev, Talaibek M. “ON EXISTENCE OF PERIODIC SOLUTIONS OF THE KDV TYPE EQUATION”. TWMS Journal of Applied and Engineering Mathematics 01/2 (December 1, 2011): 167-172. https://izlik.org/JA28CT33WH.
JAMA
1.Imanaliev TM. ON EXISTENCE OF PERIODIC SOLUTIONS OF THE KDV TYPE EQUATION. JAEM. 2011;01:167–172.
MLA
Imanaliev, Talaibek M. “ON EXISTENCE OF PERIODIC SOLUTIONS OF THE KDV TYPE EQUATION”. TWMS Journal of Applied and Engineering Mathematics, vol. 01, no. 2, Dec. 2011, pp. 167-72, https://izlik.org/JA28CT33WH.
Vancouver
1.Talaibek M. Imanaliev. ON EXISTENCE OF PERIODIC SOLUTIONS OF THE KDV TYPE EQUATION. JAEM [Internet]. 2011 Dec. 1;01(2):167-72. Available from: https://izlik.org/JA28CT33WH