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首页> 外文期刊>Journal of physics, A. Mathematical and theoretical >Kink-antikink interaction forces and bound states in a phi (4) model with quadratic and quartic dispersion
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Kink-antikink interaction forces and bound states in a phi (4) model with quadratic and quartic dispersion

机译：PHI（4）模型中的Kink-Antikink互动力和绑定状态，具有二次和四分之一分散

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摘要

We consider the interaction of solitary waves in a model involving the well-known phi (4) Klein-Gordon theory, but now bearing both Laplacian and biharmonic terms with different prefactors. As a result of the competition of the respective linear operators, we obtain three distinct cases as we vary the model parameters. In the first the biharmonic effect dominates, yielding an oscillatory inter-wave interaction; in the third the harmonic effect prevails yielding exponential interactions, while we find an intriguing linearly modulated exponential effect in the critical second case, separating the above two regimes. For each case, we calculate the force between the kink and antikink when initially separated with sufficient distance. Being able to write the acceleration as a function of the separation distance, and its corresponding ordinary differential equation, we test the corresponding predictions, finding very good agreement, where appropriate, with the corresponding partial differential equation results. Where the two findings differ, we explain the source of disparities. Finally, we offer a first glimpse of the interplay of harmonic and biharmonic effects on the results of kink-antikink collisions and the corresponding single- and multi-bounce windows.
机译：我们考虑孤立波的相互作用在一个模型涉及著名的φ（4）Klein Gordon理论，但现在承载Laplacian和双调和项与不同的预因子。由于各线性算子之间的竞争，当我们改变模型参数时，我们得到了三种不同的情况。在第一种情况下，双谐波效应占主导地位，产生振荡的波间相互作用；在第三种情况下，谐波效应占主导地位，产生指数相互作用，而在临界第二种情况下，我们发现了一个有趣的线性调制指数效应，将上述两个区域分开。对于每种情况，我们计算初始分离足够距离时扭结和反扭结之间的力。由于能够写出加速度作为分离距离的函数，以及相应的常微分方程，我们测试了相应的预测，发现在适当的情况下，与相应的偏微分方程结果非常吻合。如果这两个发现不同，我们将解释差异的来源。最后，我们提供了谐波和双谐波效应对扭结-反扭结碰撞结果的相互作用，以及相应的单反弹和多反弹窗口的第一眼。

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