- Davidson, N., (1972), Methods in Nonlinear Plasma Theory, Academic Press, New York.
- Taniuti, T., (1974), Reductive perturbation method and far field of wave equations, Progress in Theoretical Physics Supplement, 55, 1-35.
- Sugimoto, N. and Kakutani, T., (1977), Note on higher order terms in reductive perturbation theory, J. Phys. Soc. Japan, 43, 1469-1470.
- Kodama, Y. and Taniuti, T., (1978), Higher order approximation in reductive perturbation method 1. Weakly dispersive system, J. Phys. Soc. Japan, 45, 298-310.
- Washimi, H. and Taniuti, T., (1966), Propagation of ionic-acoustic solitary waves of small amplitude, Phys. Rev. Letter, 17, 996-998.
- Kraenkel, R. A., Manna, M. A. and Pereira, J. G., (1995), The Korteweg-deVries hierarchy and long water waves, J. Math. Phys., 36, 307-320.
- Malfliet, M. and Wieers, E., (1996), The theory of nonlinear ion-acoustic waves revisited, J. Plasma Phys., 56, 441-453.
- Demiray, H., (1999), A modified reductive perturbation method as applied to nonlinear ion-acoustic waves, J. Phys. Soc. Japan, 68, 1833-1837.
- Demiray, H., (2000), On the contribution of higher order terms to solitary waves in fluid-filled elastic tubes, Z. Agnew. Math. Phys. (ZAMP),51, 75-91.
- Seyler, C. E. and Fenstermacher, D. L., (1994), A symmetrical regularized-long-wave equation, Physics of Fluids, 27, 4-7.

Modified reductive perturbation method, Ion-acoustic waves, Korteweg-deVries In this work, we extended the application of ”the modified reductive perturbation method” to symmetrical regularized long waves with quadratic nonlinearity and obtained various form of KdV equations as the governing equations. Seeking a localized travelling wave solutions to these evolution equations we determined the scale parameters g1 and g2 so as to remove the possible secularities that might occur. To indicate the power and elegance of the present method, we compared our result with the exact travelling wave solution of the symmetric regularized long-wave equation with quadratic nonlinearity. These results show that for weakly nonlinear case the solutions for both approaches coincide with each other. The present method is seen to be fairly simple as compared to the renormalization method of Kodama and Taniuti [4] and the multiple scale expansion method of Kraenkel et al [6]..

- Davidson, N., (1972), Methods in Nonlinear Plasma Theory, Academic Press, New York.
- Taniuti, T., (1974), Reductive perturbation method and far field of wave equations, Progress in Theoretical Physics Supplement, 55, 1-35.
- Sugimoto, N. and Kakutani, T., (1977), Note on higher order terms in reductive perturbation theory, J. Phys. Soc. Japan, 43, 1469-1470.
- Kodama, Y. and Taniuti, T., (1978), Higher order approximation in reductive perturbation method 1. Weakly dispersive system, J. Phys. Soc. Japan, 45, 298-310.
- Washimi, H. and Taniuti, T., (1966), Propagation of ionic-acoustic solitary waves of small amplitude, Phys. Rev. Letter, 17, 996-998.
- Kraenkel, R. A., Manna, M. A. and Pereira, J. G., (1995), The Korteweg-deVries hierarchy and long water waves, J. Math. Phys., 36, 307-320.
- Malfliet, M. and Wieers, E., (1996), The theory of nonlinear ion-acoustic waves revisited, J. Plasma Phys., 56, 441-453.
- Demiray, H., (1999), A modified reductive perturbation method as applied to nonlinear ion-acoustic waves, J. Phys. Soc. Japan, 68, 1833-1837.
- Demiray, H., (2000), On the contribution of higher order terms to solitary waves in fluid-filled elastic tubes, Z. Agnew. Math. Phys. (ZAMP),51, 75-91.
- Seyler, C. E. and Fenstermacher, D. L., (1994), A symmetrical regularized-long-wave equation, Physics of Fluids, 27, 4-7.

Primary Language | English |
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Journal Section | Research Article |

Authors | |

Publication Date | June 1, 2011 |

Published in Issue | Year 2011, Volume 01, Issue 1 |

Bibtex | @ { twmsjaem761808, 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 = {1}, pages = {49 - 57}, title = {AN APPLICATION OF MODIFIED REDUCTIVE PERTURBATION METHOD TO SYMMETRIC REGULARIZED-LONG-WAVE}, key = {cite}, author = {Demiray, Hilmi} } |