标题： 耦合Boussinesq方程的弱非线性解和辐射孤立波 显示英文标题

标题： Weakly-nonlinear solution of coupled Boussinesq equations and radiating solitary waves

摘要： 弱非线性波在具有不完美界面（软结合）的分层波导中可以使用耦合Boussinesq方程进行建模。我们假设各层材料具有接近的力学性能，在这种情况下，系统可以支持辐射孤立波。我们在有限长度区间的周期函数类中考虑该问题，构建了该系统的弱非线性达朗贝尔型解。该解使用了一种涉及快速特征变量和两个慢时间变量的新多重尺度过程来构建。对该解的渐近有效性进行了数值仔细检查。我们还讨论了局部初始条件的无限区间极限情况。该解被用于研究辐射孤立波的相互作用。 显示英文摘要

摘要： Weakly-nonlinear waves in a layered waveguide with an imperfect interface (soft bonding between the layers) can be modelled using coupled Boussinesq equations. We assume that the materials of the layers have close mechanical properties, in which case the system can support radiating solitary waves. We construct a weakly-nonlinear d'Alembert-type solution of this system, considering the problem in the class of periodic functions on an interval of finite length. The solution is constructed using a novel multiple-scales procedure involving fast characteristic variables and two slow time variables. Asymptotic validity of the solution is carefully examined numerically. We also discuss the limiting case of an infinite interval for localised initial conditions. The solution is applied to study interactions of radiating solitary waves.