Integrable KdV systems: Recursion operators of degree four

Gurses, M
Karasu, Atalay
The recursion operator and bi-Hamiltonian formulation of the Drinfeld-Sokolov system are given. (C) 1999 Elsevier Science B.V.


On verification of restricted extended affine equivalence of vectorial boolean functions
Sınak, Ahmet; Özbudak, Ferruh; Yayla, Oğuz; Department of Cryptography (2012)
Vectorial Boolean functions are used as S-boxes in cryptosystems. To design inequivalent vectorial Boolean functions resistant to known attacks is one of the challenges in cryptography. Verifying whether two vectorial Boolean functions are equivalent or not is the final step in this challenge. Hence, finding a fast technique for determining whether two given vectorial Boolean functions are equivalent is an important problem. A special class of the equivalence called restricted extended affine (REA) equivale...
On construction of recursion operators from Lax representation
Gurses, M; Karasu, Atalay; Sokolov, VV (1999-12-01)
In this work we develop a general procedure for constructing the recursion operators for nonlinear integrable equations admitting Lax representation. Several new examples are given. In particular, we find the recursion operators for some KdV-type systems of integrable equations. (C) 1999 American Institute of Physics. [S0022-2488(99)03212-0].
Divisibility properties on boolean functions using the numerical normal form
Göloğlu, Faruk; Yücel, Melek D; Department of Cryptography (2004)
A Boolean function can be represented in several different forms. These different representation have advantages and disadvantages of their own. The Algebraic Normal Form, truth table, and Walsh spectrum representations are widely studied in literature. In 1999, Claude Carlet and Phillippe Guillot introduced the Numerical Normal Form. NumericalNormal Form(NNF) of a Boolean function is similar to Algebraic Normal Form, with integer coefficients instead of coefficients from the two element field. Using NNF re...
Value sets of bivariate folding polynomials over finite fields
Küçüksakallı, Ömer (2018-11-01)
We find the cardinality of the value sets of polynomial maps associated with simple complex Lie algebras B-2 and G(2) over finite fields. We achieve this by using a characterization of their fixed points in terms of sums of roots of unity.
Recursion operators of some equations of hydrodynamic type
GÜRSES, METİN; Zheltukhın, Kostyantyn (2001-03-01)
We give a general method for constructing recursion operators for some equations of hydrodynamic type, admitting a nonstandard Lax representation. We give several examples for N=2 and N=3 containing the equations of shallow water waves and its generalizations with their first two general symmetries and their recursion operators. We also discuss a reduction of N+1 systems to N systems of some new equations of hydrodynamic type. (C) 2001 American Institute of Physics.
Citation Formats
M. Gurses and A. Karasu, “Integrable KdV systems: Recursion operators of degree four,” PHYSICS LETTERS A, pp. 247–249, 1999, Accessed: 00, 2020. [Online]. Available: