# Solution of the forced korteweg-de vries- burgers nonlinear evolution equation

Tay , Kim Gaik and Chew, Yee Ming and Ong, Chee Tiong and Mohamad, Mohd Nor (2005) Solution of the forced korteweg-de vries- burgers nonlinear evolution equation. In: 2nd International Conference on Research and Education in Mathematics (ICREM 2) , 25th-27th May 2005, Universiti Putra Malaysia, Serdang.

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## Abstract

This paper reports several ﬁndings on forced solitons solution generated by the forced Korteweg-de Vries-Burgers equation (fKdVB), Ut + εUUx − νUxx + µUxxx = f(x), a≤ x ≤ b. The fKdVB equation is a nonlinear evolution equation that combines several effects such as forcing; f(x), nonlinearity; εUUx, dissipation; νUxx and dispersion; µUxxx. The forcing term breaks those symmetries associated with the unforced systems. Thus, the traditional analytical method such as inverse scattering method and B¨acklund transformation do not work on forcing system anymore. Approximate and numerical solution seem to be the ways to solve the fKdVB equation. The semi-implicit pseudo-spectral method is used to develop a numerical scheme to solve the fKdVB equation with arbitrary forcing. A software package,(BURSO) that has user friendly graphical interface is developed using Matlab 7.0 to implement the above numerical scheme. Numerical simulation proves that it is very ﬂexible since it can solve free and force system such as the KdV, Burgers, KdVB and fKdV equations eﬃciently. Thus it is able to solve the fKdVB equation faithfully. Our future research would sought the approximate solution of the fKdVB equation.

Item Type: Conference or Workshop Item (Paper) Korteweg-de Vries, Burgers, semi-implicit pseudo-spectral method,soliton Q Science > QA Mathematics Faculty of Applied Science and Technology > Department of Science and Mathematics Khairunnisa Ahmad 15 Apr 2010 07:24 21 Jan 2015 08:10 http://eprints.uthm.edu.my/id/eprint/186 View Download Statistic