摘要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.
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.
LI Yu-Qi. Interaction between Soliton and Periodic Wave[J]. 中国物理快报, 2008, 25(8): 2735-2738.
LI Yu-Qi. Interaction between Soliton and Periodic Wave. Chin. Phys. Lett., 2008, 25(8): 2735-2738.
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