The method of nonlinearization of Lax pair for the classical integrable (1+1)-dimensional system has aroused strong interests in soliton theory, including mono-nonlinearization [1, 2, 3] and binary nonlinearization [4, 5]. The crucial technique is to find constraints between the potentials (i. e, functions of soliton equation) and the eigenfunctions of the spectral problem associated with the s...

The tri-Hamiltonian method is applied to the Merola-Ragnisco-Tu equation. This enables us construct a new integrable system, whose continuum limit related AKNS system. Moreover, system proved have linear spectral problems (Lax pair), bi-Hamiltonian structure and Darboux-Bäcklund transformation. Through transformation, we some exact solutions for

We investigate the mKdV hierarchy with integral type of source (mKdVHWS), which consist of the reduced AKNS eigenvalue problem with r = q and the mKdV hierarchy with extra term of the integration of square eigenfunction. First we propose a method to find the explicit evolution equation for eigenfunction of the auxiliary linear problems of the mKdVHWS. Then we determine the evolution equations o...

Abstract. Binary symmetry constraints are applied to constructing Bäcklund transformations of soliton systems, both continuous and discrete. Construction of solutions to soliton systems is split into finding solutions to lowerdimensional Liouville integrable systems, which also paves a way for separation of variables and exhibits integrability by quadratures for soliton systems. Illustrative ex...

Wewill discuss how to generate integrable couplings from zero curvature equations associated with matrix spectral problems. The key elements are matrix loop algebras consisting of block matrices with blocks of the same size or different sizes. Hamiltonian structures are furnished by applying the variational identity defined over semi-direct sums of Lie algebras. Illustrative examples include in...