论文标题
与对数非线性的相对论模型中的纠结
Kinks in the relativistic model with logarithmic nonlinearity
论文作者
论文摘要
我们研究具有对数非线性的相对论模型的性质。我们表明，此类模型允许两种类型的解决方案：拓扑上的（高卢斯）和拓扑上的非平凡（扭结），具体取决于非线性耦合的迹象。我们主要关注扭结案例并研究其散射特性。对于扭结 - 安丁基克散射，我们发现了初始速度的临界值，该速度将两种不同的散射情况分开。对于低于此临界值的初始速度，扭结形成一个结合状态，然后衰减缓慢。如果初始速度高于临界值，则扭结碰撞，反弹并最终逃到无限态度。在此过程中，较高的初始速度是碰撞的弹性越大。我们还研究了纠结溶液的激发谱。
We study the properties of a relativistic model with logarithmic nonlinearity. We show that such model allows two types of solutions: topologically trivial (gaussons) and topologically non-trivial (kinks), depending on a sign of the nonlinear coupling. We focus primarily on the kinks' case and study their scattering properties. For the kink-antikink scattering, we have found a critical value of the initial velocity, which separates two different scenarios of scattering. For the initial velocities below this critical value, the kinks form a bound state, which then decays slowly. If the initial velocities are above the critical value, the kinks collide, bounce and eventually escape to infinities. During this process, the higher initial velocity is, the greater is the elasticity of the collision. We also study excitation spectrum of the kink solution.
