6 papers
Indecomposable involutive set-theoretic solutions of the Yang-Baxter equation and orthogonal dynamical extensions of cycle sets
Marco Castelli, Francesco Catino, Paola Stefanelli
Employing the algebraic structure of the left brace and the dynamical extensions of cycle sets, we investigate a class of indecomposable involutive set-theoretic solutions of the Y…
Left non-degenerate set-theoretic solutions of the Yang-Baxter equation and dynamical extensions of q-cycle sets
Marco Castelli, Francesco Catino, Paola Stefanelli
A first aim of this paper is to give sufficient conditions on left non-degenerate bijective set-theoretic solutions of the Yang-Baxter equation so that they are non-degenerate. In…
On the indecomposable involutive set-theoretic solutions of the Yang-Baxter equation of prime-power size
Marco Castelli, Giuseppina Pinto, Wolfgang Rump
We develop a method to construct all the indecomposable involutive set-theoretic solutions of the Yang-Baxter equation with a prime-power number of elements and cyclic permutation…
Modified Zakharov-Kuznetsov equation on rectangles
Marcos Castelli, Gleb Doronin
Initial-boundary value problem for the modified Zakharov-Kuznetsov equation posed on a bounded rectangle is considered. The main difficulty is the critical power in nonlinear term.…
Subcritical and critical generalized Zakharov-Kuznetsov equation posed on bounded rectangles
Marcos Castelli, Gleb Doronin
Initial-boundary value problem for the generalized Zakharov-Kuznetsov equation posed on a bounded rectangle is considered. Critical and subcritical powers in nonlinearity are studi…
About a question of Gateva-Ivanova and Cameron on square-free set-theoretic solutions of the Yang-Baxter equation
Marco Castelli, Francesco Catino, Giuseppina Pinto
In this paper, we introduce a new sequence to find a new estimation of the cardinality of the minimal involutive square-free solution of level . As an applicat…