International Conference on Mechanical and Electrical Technology, 3rd, (ICMET-China 2011), Volumes 1–3
286 A Family of New Evtegrable Couplings with Four Potential Functions of C-KdV Hierarchy
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Searching for new integrable couplings of the known integrable hierarchies of evolution equations is a quite new interesting aspect and is of great significance in solution theory. In this paper, a new loop algebra and its basis are first presented. Second a new isospectral problem with four potentials in the loop algebra is considered to construct integrable couplings of the the well-known C-KdV hierarchy by the zero-curvature equation. In particular, we obtain a special integrable couplings equations of the C-KdV equation.