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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…