Summary
In the present paper, the Lax representations of the equations of the coupled KdV type are obtained. By making use of a constrained relation between the potential and the eigenfunctions of the spectral problem, the Lax representations are nonlinearized. If one introduces a suitable symplectic structure on a complex space by means of an invertible linear mapping from the real to the complex space, then the nonlinearized Lax pairs become exactly the commutable flows of a finite-dimensional completely iterable system in the Liouville sense. Moreover, the representations of solutions of the equations of the coupled KdV type are given.
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Baocai, Z., Zhuquan, G. The involutive representation of solutions of the coupled KdV equation. Nuov Cim B 107, 855–862 (1992). https://doi.org/10.1007/BF02899287
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DOI: https://doi.org/10.1007/BF02899287