Nonlinear continuous integrable Hamiltonian couplings

Bi-integrable couplings of a Kaup–Newell type soliton hierarchy and their bi-Hamiltonian structures

“…Upon observation of the bi-Hamiltonian structures (2.21) and differential orders of the sequence fa i ; b i ; c i ji P 1g, we can state that the soliton hierarchy (2.14) is Liouville integrable [37][38][39][40][41]. Every member in the hierarchy (2.14) possesses infinitely many independent commuting conserved functionals…”

Nonlinear Super Integrable Couplings of Super Classical Boussinesq Hierarchy

“…One approach to construct linear integrable couplings of the classical soliton equation are presented by using matrix Lie algebra constructing new loop Lie algebra [13]. Recently, Ma and Zhu [14], [15] presented a scheme for constructing nonlinear continuous and discrete integrable couplings using the block type matrix algebra. However, there is one interesting question for us is how to generate nonlinear super integrable couplings for the super integrable hierarchy.…”

Nonlinear Super Integrable Couplings of Super Yang Hierarchy and Its Super Hamiltonian Structures

“…A few approaches to construct linear integrable couplings of the classical soliton equation are presented by permutation, enlarging spectral problem, using matrix Lie algebra [12] constructing new loop Lie algebra and creating semi-direct sums of Lie algebra.…”

“…There search of integrable couplings of the well known integrable hierarchy has received considerable attention [10] [11] [12]. A few approaches to construct linear integrable couplings of the classical soliton equation are presented by permutation, enlarging spectral problem, using matrix Lie algebra [12] constructing new loop Lie algebra and creating semi-direct sums of Lie algebra.…”