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Numerical study of a nonlinear integrodifferential equation

Authors:

Zhu Yong

Institution:

Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, P. R. China

Abstract:

In this paper, by using the pseudo-spectral method of Fornberg and Whitham, a nonlinear integrodifferential equations

$A_t + 6AA_x + \frac{1}{{2\left| {\ln \varepsilon } \right|}}\int_{ - \infty }^{ + \infty } {\frac{{A(x',t)}}{{\left\{ {(x' - x)^2 + \varepsilon ^2 } \right\}^{1/2} }}dx'} = 0$

is investigated numerically. It is found that for small ∈, the result is close to that of the KdV equation, whereas the effects of larger ∈ and the initial condition are significant. Project supported by National and Shanghai Educational Committee

Keywords:

integrodifferential equation spectral method solitary waves

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