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Numerical Methods for Bi-Directional-Soliton Problems

Unlike KdV equation, numerical methods for solving Bidirectional-soliton: U t+F(U) x=cU xxx and little work has been done on this problem. After numerical simulation by several methods, it is found that the leepfrog differential scheme with small-stencil pade method performs better. A filter and an implicit scheme are adopted to solve the instability problem of non-linear dispersive equation and the numerical results are satisfactory.