we show that a recently introduced lax pair of the sawada-kotera equation is nota new one but is trivially related to the known old lax pair. using the so-called trivialcompositions of the old lax pairs with a differentially constrained arbitrary operators,we give some examples of trivial lax pairs of kdv and sawada-kotera equations.

M-branes are related to theories on function spaces A involving M-linear non-commutative maps from A × · · · × A to A. While the Lie-symmetry-algebra of volume preserving diffeomorphisms of T cannot be deformed when M > 2, the arising M-algebras naturally relate to Nambu’s generalisation of Hamiltonian mechanics, e.g. by providing a representation of the canonical M-commutation relations, [J1, ...

On the one hand, we put in evidence new symmetry operators of the nonlinear Korteweg-de Vries equation by exploiting its Lax form expressed in terms of a pair of linear equations. A KdV supersymmetric version is also studied in order to determine its symmetry Lie superalgebra. On the other hand, nonlinear sl(2)-algebras are then visited and new unitary irreducible representations are characteri...

We consider the Lax representation of the new two-component coupled integrable system recently discovered by the author. Connection of the hierarchy of infinitely many Lax pairs with each other is presented.

Generalizing our recent joint paper with Vasily Pestun (arXiv:2001.04929), we construct a family of $SO(2r),Sp(2r),SO(2r+1)$ rational Lax matrices, polynomial in the spectral parameter, parametrized by divisors on projective line coefficients being dominant integral coweights associated Lie algebras. To this end, provide RTT realization antidominantly shifted extended Drinfeld Yangians $\mathfr...

In this work we develop some aspects of the theory of Hopf algebras to the context of autonomous map pseudomonoids. We concentrate in the Hopf modules and the Centre or Drinfel’d double. If A is a map pseudomonoid in a monoidal bicategory M , the analogue of the category of Hopf modules for A is an Eilenberg-Moore construction for a certain monad in Hom(M op,Cat). We study the existence of the ...

We consider the problem of realizing hyperbolicity cones as spectrahedra, i.e. as linear slices of cones of positive semidefinite matrices. The generalized Lax conjecture states that this is always possible. We use generalized Clifford algebras for a new approach to the problem. Our main result is that if −1 is not a sum of hermitian squares in the Clifford algebra of a hyperbolic polynomial, t...

Notions of generalized multicategory have been defined in numerous contexts throughout the literature, and include such diverse examples as symmetric multicategories, globular operads, Lawvere theories, and topological spaces. In each case, generalized multicategories are defined as the “lax algebras” or “Kleisli monoids” relative to a “monad” on a bicategory. However, the meanings of these wor...