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Integrable 2+1 Dimensional Equations, Their Recursion Operators and Bi-Hamiltonian Structures as Reduction of Multidimensional Systems

机译：可积2 + 1维方程，它们的递归算子和双哈密顿结构作为多维系统的约简

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摘要

Multidimensional equations are derived from the compatibility condition between linear operators. The algebraic properties associated with their recursion operators and bi-Hamiltonian structures are summarized. A dimensional reduction is used to derive known integrable equations in 2+1 dimensions like the Kadomtsev-Petviashvili equation; the main aspects of the theory associated with their recursion and bi-Hamiltonian operators are also obtained through this reduction procedure.

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作者
Santini, P. M.;
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年度 1987
页码 p.1-18
总页数 18
原文格式 PDF
正文语种 eng
中图分类工业技术;
关键词
Hamiltonian functions; Recursive functions; Numerical integration; Operators (Mathematics); Optimization; Dynamical systems; Lattices (Mathematics);

机译：哈密顿函数;递归函数;数值积分;算子（数学）;优化;动力系统;格子（数学）;

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1. Lax pairs, recursion operators and bi-Hamiltonian representations of (3+1)-dimensional Hirota type equations [J] . Sheftel M. B., Yazici D. Journal of geometry and physics . 2019,第期

机译：LAX对，递归操作员和BI-HAMILTONIAN表示（3 + 1）-Dimensional Hirota类型方程
2. Integrable evolution systems based on Gerdjikov-Ivanov equations, bi-Hamiltonian structure, finite-dimensional integrable systems and N-fold Darboux transformation [J] . Fan EG. Journal of Mathematical Physics . 2000,第11期

机译：基于Gerdjikov-Ivanov方程，双哈密尔顿结构，有限维可积系统和N折Darboux变换的可积演化系统
3. Symmetry reduction of the first heavenly equation and $2+1$-dimensional bi-Hamiltonian system [J] . DEVR?M YAZICI Turkish journal of physics . 2018,第2期

机译：第一个天堂方程和$ 2 + 1 $维Bi-Hamiltonian系统的对称约简
4. NONCLASSICAL SYMMETRY REDUCTIONS OF THE CALOGERO-DEGASPERIS-FOKAS EQUATION IN (2+1) DIMENSIONS [C] . M.L. GANDARIAS, S. SAEZ Meeting on Waves and Stability in Continuous Media . 2006

机译：（2 + 1）尺寸中的Calogero-Degasperis-Fokas方程的非生效对称减少
5. Whitham Modulation Theory for Multidimensional Evolution Equations; Derivation of Integrable Systems via the Dressing Method [D] . Wang, Qiao. 2018

机译：多维演化方程的Whitham调制理论；通过修整法推导可积系统
6. Rational Recursion Operators for Integrable Differential–Difference Equations [O] . Sylvain Carpentier, Alexander V. Mikhailov, Jing Ping Wang -1

机译：可积微分方程的有理递归运算符
7. Evolutionary Hirota type (2+1)-dimensional equations: Lax pairs, recursion operators and bi-Hamiltonian structures [O] . Sheftel, Mikhail B., Yazici, Devrim 2017

机译：进化Hirota型（2 + 1）维方程：Lax对，递归算子和双哈密顿结构
8. Integrable Equations in Multi-Dimensions (2+1) are Bi-Hamiltonian Systems [R] . Fokas, A. S., Santini, P. M. 1987

机译：多维（2 + 1）中的可积方程是双哈密顿系统

Integrable 2+1 Dimensional Equations, Their Recursion Operators and Bi-Hamiltonian Structures as Reduction of Multidimensional Systems

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