Recursion Operators of Some Equations of Hydrodynamic Type
نویسنده
چکیده
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 higher symmetries and their recursion operators. We also discuss a reduction of N + 1 systems to N systems of some new equations of hydrodynamic type.
منابع مشابه
2 00 1 Group analysis of hydrodynamic - type systems
We study point and higher symmetries for the hydrodynamic-type systems with two independent variables t and x with and without explicit dependence of the equations on t, x. We consider those systems which possess an infinite group of the hy-drodynamic symmetries, establish existence conditions for this property and, using it, derive linearizing transformations for these systems. The recursion o...
متن کاملSymmetry group analysis and invariant solutions of hydrodynamic-type systems
We study point and higher symmetries of systems of the hydrodynamic type with and without an explicit dependence on t,x. We consider such systems which satisfy the existence conditions for an infinite-dimensional group of hydrodynamic symmetries which implies linearizing transformations for these systems. Under additional restrictions on the systems, we obtain recursion operators for symmetries...
متن کاملA Generalization of the Meir-Keeler Condensing Operators and its Application to Solvability of a System of Nonlinear Functional Integral Equations of Volterra Type
In this paper, we generalize the Meir-Keeler condensing operators via a concept of the class of operators $ O (f;.)$, that was given by Altun and Turkoglu [4], and apply this extension to obtain some tripled fixed point theorems. As an application of this extension, we analyze the existence of solution for a system of nonlinear functional integral equations of Volterra type. Finally, we p...
متن کاملOn construction of recursion operators from Lax representation
In this work we develop a general procedure for constructing the recursion operators for non-linear 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.
متن کاملNonlocal Hamiltonian operators of hydrodynamic type with flat metrics, integrable hierarchies and the equations of associativity
In this paper we solve the problem of describing all nonlocal Hamiltonian operators of hydrodynamic type with flat metrics and establish that this nontrivial special class of Hamiltonian operators is closely connected with the associativity equations of twodimensional topological quantum field theories and the theory of Frobenius manifolds. It is shown that the Hamiltonian operators of this cla...
متن کامل