- Y. S. Kivshar and B. A. Malomed, (1989), Dynamics of solitons in nearly integrable systems, Review of Modern Physics, 61, pp. 763-915.
- J. Engelbrecht, (1991), Solutions to the perturbed KdV equation, Wave Motion, 14, pp. 85-92.
- G. L. Lamb Jr, (1980), Elements of Soliton Theory, Wiley, New York.
- H. Demiray, (2002), A note on the solution of perturbed Korteweg-deVries equation, Appl. Math. Computation, 132, pp. 643-647.
- J. K. Xue, (2002), Modulation of dust acoustic waves with non-adiabatic dust charge fluctuations, Phys. Lett. A, 320, pp. 226-233.
- H. Demiray, (2003), An analytical solution to the dissipative nonlinear Schr¨odinger equation, Appl. Mat. Computation, 145, pp. 179-184.

In the present work, we modied the conventional "weighted residual method" to some nonlinear evolution equations and tried to obtain the approximate progressive wave solutions for these evolution equations. For the illustration of the method we studied the approximate progressive wave solutions for the perturbed KdV and the dissipative NLS equations. The results obtained here are in complete agreement with the solutions of inverse scattering method. The present solutions are even valid when the dissipative eects are considerably large. The results obtained are encouraging and the method can be used to study the cylindrical and spherical evolution equations.

- Y. S. Kivshar and B. A. Malomed, (1989), Dynamics of solitons in nearly integrable systems, Review of Modern Physics, 61, pp. 763-915.
- J. Engelbrecht, (1991), Solutions to the perturbed KdV equation, Wave Motion, 14, pp. 85-92.
- G. L. Lamb Jr, (1980), Elements of Soliton Theory, Wiley, New York.
- H. Demiray, (2002), A note on the solution of perturbed Korteweg-deVries equation, Appl. Math. Computation, 132, pp. 643-647.
- J. K. Xue, (2002), Modulation of dust acoustic waves with non-adiabatic dust charge fluctuations, Phys. Lett. A, 320, pp. 226-233.
- H. Demiray, (2003), An analytical solution to the dissipative nonlinear Schr¨odinger equation, Appl. Mat. Computation, 145, pp. 179-184.

Primary Language | English |
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Journal Section | Research Article |

Authors | |

Publication Date | December 1, 2019 |

Published in Issue | Year 2019, Volume 9, Issue 4 |

Bibtex | @ { twmsjaem760950, 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 = {2019}, volume = {9}, number = {4}, pages = {786 - 791}, title = {AN APPROXIMATE WAVE SOLUTION FOR PERTURBED KDV AND DISSIPATIVE NLS EQUATIONS: WEIGHTED RESIDUAL METHOD}, key = {cite}, author = {Demiray, H.} } |