论文标题
多维连续TODA类型系统的粒子状，dyx又固醇和Trix共轴心谎言结构
Particle-like, dyx-coaxial and trix-coaxial Lie algebra structures for a multi-dimensional continuous Toda type system
论文作者
论文摘要
我们证明，使用$（2+1）$ - 尺寸TODA类型系统是相关的代数骨架，它是Dyons和Triadons类型的类似粒子的Lie代数（兼容组装）。我们从某些特定选择的代数骨骼中为系统获得了系统的Trix又二轴和Dyx固定谎言代数结构。特别是，通过绝对并行性的首选，我们与$（2+1）$ - 尺寸TODA类型系统相关联，由两个（兼容的）基本三合会制成的Trix-Coaxial Lie代数结构，构成了$ 2 $ -CATENA。此外，通过绝对平行性的第二选择，我们将由两个（兼容）基础底型牛群制成的dyx又固定谎言结构以及由单个$ 3 $ -DOYON制成的类似粒子的Lie代数结构。解决了一些与特殊解决方案有关的应用程序的明确示例，以及逆光谱问题。
We prove that with a $(2+1)$-dimensional Toda type system are associated algebraic skeletons which are (compatible assemblings) of particle-like Lie algebras of dyons and triadons type. We obtain trix-coaxial and dyx-coaxial Lie algebra structures for the system from algebraic skeletons of some particular choice for compatible associated absolute parallelisms. In particular, by a first choice of the absolute parallelism, we associate with the $(2+1)$-dimensional Toda type system a trix-coaxial Lie algebra structure made of two (compatible) base triadons constituting a $2$-catena. Furthermore, by a second choice of the absolute parallelism, we associate a dyx-coaxial Lie algebra structure made of two (compatible) base dyons, as well as particle-like Lie algebra structures made of single $3$-dyons. Some explicit examples of applications such as conservation laws related to special solutions, and an inverse spectral problem are worked out.
