Recursion operators of some equations of hydrodynamic type

Zheltukhın, Kostyantyn
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.


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].
Abundance of Real Lines on Real Projective Hypersurfaces
Finashin, Sergey (2013-01-01)
We show that a generic real projective n-dimensional hypersurface of degree 2n-1 contains many real lines, namely not less than (2n-1)!!, which is approximately the square root of the number of complex lines. This estimate is based on the interpretation of a suitable signed count of the lines as the Euler number of an appropriate bundle.
Integrable KdV systems: Recursion operators of degree four
Gurses, M; Karasu, Atalay (1999-01-25)
The recursion operator and bi-Hamiltonian formulation of the Drinfeld-Sokolov system are given. (C) 1999 Elsevier Science B.V.
Cyclic codes and reducible additive equations
Guneri, Cem; Özbudak, Ferruh (Institute of Electrical and Electronics Engineers (IEEE), 2007-02-01)
We prove a Weil-Serre type bound on the number of solutions of a class of reducible additive equations over finite fields. Using the trace representation of cyclic codes, this enables us to write a general estimate for the weights of cyclic codes. We extend Woffmann's weight bound to a larger classes of cyclic codes. In particular, our result is applicable to any cyclic code over F-p and F-p2, where p is an arbitrary prime. Examples indicate that our bound performs very well against the Bose-Chaudhuri-Hocqu...
Solving Constrained Optimal Control Problems Using State-Dependent Factorization and Chebyshev Polynomials
Gomroki, Mohammad Mehdi; Topputo, Francesco; Bernelli-Zazzera, Franco; Tekinalp, Ozan (2018-03-01)
The present work introduces a method to solve constrained nonlinear optimal control problems using state-dependent coefficient factorization and Chebyshev polynomials. A recursive approximation technique known as approximating sequence of Riccati equations is used to replace the nonlinear problem by a sequence of linear-quadratic and time-varying approximating problems. The state variables are approximated and expanded in Chebyshev polynomials. Then, the control variables are written as a function of state ...
Citation Formats
M. GÜRSES and K. Zheltukhın, “Recursion operators of some equations of hydrodynamic type,” JOURNAL OF MATHEMATICAL PHYSICS, pp. 1309–1325, 2001, Accessed: 00, 2020. [Online]. Available: