Departamento de Física-Química, Instituto de Física, Universidad Nacional Autónoma de México, México, D.F., C.P. 04510, Mexico.
Chaos. 2012 Sep;22(3):033145. doi: 10.1063/1.4752244.
We consider solitons in a system of linearly coupled Korteweg-de Vries (KdV) equations, which model two-layer settings in various physical media. We demonstrate that traveling symmetric solitons with identical components are stable at velocities lower than a certain threshold value. Above the threshold, which is found exactly, the symmetric modes are unstable against spontaneous symmetry breaking, which gives rise to stable asymmetric solitons. The shape of the asymmetric solitons is found by means of a variational approximation and in the numerical form. Simulations of the evolution of an unstable symmetric soliton sometimes produce its breakup into two different asymmetric modes. Collisions between moving stable solitons, symmetric and asymmetric ones, are studied numerically, featuring noteworthy features. In particular, collisions between asymmetric solitons with identical polarities are always elastic, while in the case of opposite polarities the collision leads to a switch of the polarities of both solitons. Three-soliton collisions are studied too, featuring quite complex interaction scenarios.
我们研究了线性耦合 Korteweg-de Vries（KdV）方程组中的孤子，这些方程组可用于各种物理介质中的双层设置。我们证明了速度低于一定阈值时，具有相同分量的 travelling symmetric solitons 是稳定的。在高于阈值的情况下，对称模式会自发地打破对称性，从而产生稳定的不对称孤子。不对称孤子的形状通过变分近似和数值形式找到。不稳定对称孤子的演化模拟有时会导致其分裂成两个不同的不对称模式。数值研究了移动稳定孤子（对称和不对称的）之间的碰撞，具有显著的特征。特别是，具有相同极性的不对称孤子之间的碰撞总是弹性的，而在极性相反的情况下，碰撞会导致两个孤子的极性发生转换。我们还研究了三孤子碰撞，具有相当复杂的相互作用场景。
