On the propagation of solitary pulses in microstructured materials. (English) Zbl 1111.74026
Summary: KdV-type evolution equation, including the third- and the fifth-order dispersive and fourth-order nonlinear terms, is used for modelling the wave propagation in microstructured solids like martensitic-austenitic alloys. The character of the dispersion depends on the signs of the third- and the fifth-order dispersion parameters. In the paper the model equation is solved numerically under localised initial conditions in the case of mixed dispersion, i.e., the character of dispersion is normal for some wavenumbers and anomalous for others. Two types of solution are defined and discussed. Relatively small solitary waves result in irregular solution. However, if the amplitude exceeds a certain threshold, a solution having regular time-space behaviour emerges. The latter has tree sub-types: “plaited” solitons, two solitary waves and single solitary wave. Depending on the value of the amplitude of the initial pulse, these sub-types can appear alone or in a certain sequence.
MSC:
| 74J35 | Solitary waves in solid mechanics |
References:
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