可积非线性Majorana型旋量模型的相对论耗散
Relativistic dissipatons in integrable nonlinear Majorana type spinor model
摘要：
利用活动标架方法，引入了1+1维实Majorana型旋量场的相对论可积非线性模型，并建立了该模型与单叶双曲面上Papanicolau旋量模型的规范等价性.根据所谓的双对数，该模型也被表示为双曲复相对论模型，其形式类似于有质量的Thirring模型。利用Hirota双线性方法构造了该模型的一个耗散解。我们计算了这种耗散子的第一阶运动积分，表明它代表了具有高度非线性质量的相对论粒子。分析了两个相对论耗散子散射的共振条件，得到了描述耗散子共振性质的解。
英文摘要：
By method of moving frame, the relativistic integrable nonlinear model for real, Majorana type spinor fields in 1+1 dimensions is introduced and gauge equivalence of this model with Papanicolau spin model on one sheet hyperboloid is established. In terms of the so called double numbers, the model is represented also as hyperbolic complex relativistic model, in the form similar to the massive Thirring model. By using Hirota bilinear method, one dissipaton solution of this model is constructed. We calculated first integrals of motion for this dissipaton and show that it represents relativistic particle with highly nonlinear mass. Analyzing resonance conditions for scattering of two relativistic dissipatons, we find a solution describing resonant property of the dissipatons.
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