Bäcklund-Transformation-Related Recursion Operators: Application to the Self-Dual Yang–Mills Equation
نویسندگان
چکیده
By using the self-dual Yang-Mills (SDYM) equation as an example, we study a method for relating symmetries and recursion operators of two partial differential equations connected to each other by non-auto-Backlund transformation. We prove Lie-algebra isomorphism between SDYM those potential (PSDYM) equation, describe construction these systems. Using certain known aspects PSDYM symmetry algebra, draw conclusions regarding Lie algebraic structure "potential symmetries" equation.
منابع مشابه
Bäcklund Transformation for the Krichever-novikov Equation
The Krichever-Novikov equation u t = u xxx − 3 2u x (u 2 xx − r(u)) + cu x , r (5) = 0 (1) appeared (up to change u = p(˜ u), ˙ p 2 = r(p)) in [1] for the first time in connection with study of finite-gap solutions of the Kadomtsev-Petviashvili equation. The distinctive feature of the equation (1) is that, accordingly to [2], no differential substitution exists connecting it with other KdV-type...
متن کاملApplication of differential transformation method to the fisher equation.
In this paper, the dierential transform method (DTM) is applied to the Fisherequation. This method can be used to obtain the exact solutions of Fisherequation. Finally, we give some examples to illustrate the suciency of themethod for solving such nonlinear partial dierential equations. These resultsshow that this technique is easy to apply.
متن کاملapplication of di fferential transformation method to the fisher equation.
in this paper, the di erential transform method (dtm) is applied to the fisherequation. this method can be used to obtain the exact solutions of fisherequation. finally, we give some examples to illustrate the suciency of themethod for solving such nonlinear partial di erential equations. these resultsshow that this technique is easy to apply.
متن کاملReducibility of zero curvature representations with application to recursion operators
We present a criterion for reducibility of zero curvature representations to a solvable subalgebra, hence to a chain of conservation laws. Our results are applied to inversion of recursion operators.
متن کاملAdding Recursion to Graph Transformation
In this paper we define recursive rules in the double pushout approach (DPO) to graph transformation. Classical DPO rules are extended with a base case condition and a recursion condition. Mechanisms are provided to pass the match from both conditions to the rule’s left hand side, and also between two consecutive steps in the recursion. The approach is useful when recursive structures (such as ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Nonlinear Mathematical Physics
سال: 2021
ISSN: ['1776-0852', '1402-9251']
DOI: https://doi.org/10.1142/s1402925110000581