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Interaction between Soliton and Periodic Wave |
| LI Yu-Qi |
| Center for Nonlinear Science, Ningbo University, Ningbo 315211 |
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LI Yu-Qi 2008 Chin. Phys. Lett. 25 2735-2738 |
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Abstract A truncation for the Laurent series in the Painlevé analysis of the KdV equation is restudied. When the truncation occurs the singular manifold satisfies two compatible fourth-order PDEs, which are homogeneous of degree 3. Both of the PDEs can be factored in the operator sense. The common factor is a third-order PDE, which is homogeneous of degree 2. The first few invariant manifolds of the third-order PDE are studied. We find that the invariant manifolds of the third-order PDE can be obtained by factoring the invariant manifolds of the KdV equation. A numerical solution of the third-order PDE is also presented. The solution reveals some interesting facts about the third-order PDE.
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02.30.Ik
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Received: 19 May 2008
Published: 25 July 2008
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