论文标题
AB方程的非独立和准积分变形
Non-holonomic and Quasi-integrable deformations of the AB Equations
论文作者
论文摘要
对于耦合方程式的AB系统，首次获得了非独立和准积分变形。 AB系统模型地球物理和大气流体运动以及非线性光学中的超短脉冲传播，并用作众所周知的正弦仪方程的概括。非全面变形保留了受高阶差异约束的可集成性，而准AB系统部分偏离了集成性，其特征是无限的数量子集（电荷）仅保守，仅在溶液中均具有渐近的差异。获得了AB系统的这两种变形的特定局部解决方案，其中一些在相应的变形上是质量上独特的，显示出与物理观察到的激发的相似性。
For the first time, both non-holonomic and quasi-integrable deformations are obtained for the AB system of coupled equations. The AB system models geophysical and atmospheric fluid motion along with ultra-short pulse propagation in nonlinear optics and serves as a generalization of the well-known sine-Gordon equation. The non-holonomic deformation retains integrability subjected to higher-order differential constraints whereas the quasi-AB system, which is partially deviated from integrability, is characterized by an infinite subset of quantities (charges) that are conserved only asymptotically given the solution possesses definite space-time parity properties. Particular localized solutions to both these deformations of the AB system are obtained, some of which are qualitatively unique to the corresponding deformation, displaying similarities with physically observed excitations.
