关于四阶晶格Gel'fand-Dikii方程

IF 0.9 3区物理与天体物理 Q2 MATHEMATICS

Symmetry Integrability and Geometry-Methods and Applications Pub Date : 2022-06-29 DOI:10.3842/SIGMA.2023.007

Guesh Yfter Tela, Songlin Zhao, Da‐jun Zhang

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引用次数: 1

摘要

研究了四边形形式的四阶格Gel’fand- dikii方程。利用直接线性化方法，给出了一些扩展晶格Gel’fand- dikii型方程。这些方程与四次离散色散关系有关，可以看作是扩展晶格Boussinesq型方程的高阶成员。这里给出的晶格方程是五分量形式的，其中一些通过引入额外的方程是多维一致的。利用直接线性化方案和多维一致性讨论了松弛可积性。考虑了五分量晶格方程的一些约简形式。

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On the Fourth-Order Lattice Gel'fand-Dikii Equations

The fourth-order lattice Gel'fand-Dikii equations in quadrilateral form are investigated. Utilizing the direct linearization approach, we present some equations of the extended lattice Gel'fand-Dikii type. These equations are related to a quartic discrete dispersion relation and can be viewed as higher-order members of the extended lattice Boussinesq type equations. The resulting lattice equations given here are in five-component form, and some of them are multi-dimensionally consistent by introducing extra equations. Lax integrability is discussed both by direct linearization scheme and also through multi-dimensional consistent property. Some reductions of the five-component lattice equations to the four-component forms are considered.

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来源期刊

Symmetry Integrability and Geometry-Methods and Applications 物理-物理：数学物理

CiteScore

1.80

自引率

0.00%

发文量

审稿时长

4-8 weeks

期刊介绍： Scope Geometrical methods in mathematical physics Lie theory and differential equations Classical and quantum integrable systems Algebraic methods in dynamical systems and chaos Exactly and quasi-exactly solvable models Lie groups and algebras, representation theory Orthogonal polynomials and special functions Integrable probability and stochastic processes Quantum algebras, quantum groups and their representations Symplectic, Poisson and noncommutative geometry Algebraic geometry and its applications Quantum field theories and string/gauge theories Statistical physics and condensed matter physics Quantum gravity and cosmology.