The propagation of localised (in space-time) waves is analysed in the context of the dynamic theory of incompressible hyperelastic solids subject to body forces corresponding to a dual power-law substrate potential. A broad class of exact solutions is obtained which, under the assumption of slow modulation, incorporates Helmholtz-type solitary waves. The linear stability of these solutions is studied under the assumption that the speed of propagation of the wave is small enough compared to the speed at which transverse waves travel in the linear regime and in the absence of external actions.

中文翻译：

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非线性弹性动力学中的亥姆霍兹型孤波解

在不可压缩的超弹性固体动力学理论的背景下，分析了局部（时空）波的传播，该理论受到与双幂律衬底电势相对应的体力的作用。在假定慢速调制的情况下，获得了广泛的精确解，其中包含了亥姆霍兹型孤波。这些解决方案的线性稳定性是在假设波的传播速度与横向波在线性状态下且没有外部作用的情况下传播的速度相比足够小的前提下研究的。