On Recursion Operators

نویسندگان

  • Jan A. Sanders
  • Jing Ping Wang
چکیده

We observe that application of a recursion operator of Burgers equation does not produce the expected symmetries. This is explained by the incorrect assumption that D−1 x Dx = 1. We then proceed to give a method to compute the symmetries using the recursion operator as a first order approximation.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Structured recursion for non-uniform data-types

Recursion is a simple but powerful programming technique used extensively in functional languages. For a number of reasons, however, it is often desirable to use structured forms of recursion in programming, encapsulated in so-called recursion operators, in preference to unrestricted recursion. In particular, using recursion operators has proved invaluable for transforming and reasoning about f...

متن کامل

Another Look on Recursion Operators

Recursion operators of partial diierential equations are identiied with BB acklund auto-transformations of linearized diieties. Relations to the classical concept and its recent Guthrie's generalization are discussed. Traditionally,a recursion operator of a PDE is a linear operator L acting on symmetries: if f is a symmetry then so is Lf. This provides a convenient way to generate innnite famil...

متن کامل

On 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 کامل

On recursion operators and nonlocal symmetries of evolution equations

We consider the recursion operators with nonlocal terms of special form for evolution systems in (1+1) dimensions, and extend them to well-defined operators on the space of nonlocal symmetries associated with the so-called universal Abelian coverings over these systems. The extended recursion operators are shown to leave this space invariant. These results apply, in particular, to the recursion...

متن کامل

On recursion operators and nonlocal symmetries of evolution equations1

We consider the recursion operators with nonlocal terms of special form for evolution systems in (1 + 1) dimensions, and extend them to well-defined operators on the space of nonlocal symmetries associated with the so-called universal Abelian coverings over these systems. The extended recursion operators are shown to leave this space invariant. These results apply, in particular, to the recursi...

متن کامل

On recursion operators for elliptic models

New quasilocal recursion and Hamiltonian operators for the Krichever-Novikov and the LandauLifshitz equations are found. It is shown that the associative algebra of quasilocal recursion operators for these models is generated by a couple of operators related by an elliptic curve equation. A theoretical explanation of this fact for the Landau-Lifshitz equation is given in terms of multiplicators...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2007