Chirality in the plane. (English) Zbl 1481.74046
Summary: It is well-known that many three-dimensional chiral material models become non-chiral when reduced to two dimensions. Chiral properties of the two-dimensional model can then be restored by adding appropriate two-dimensional chiral terms. In this paper we show how to construct a three-dimensional chiral energy function which can achieve two-dimensional chirality induced already by a chiral three-dimensional model. The key ingredient to this approach is the consideration of a nonlinear chiral energy containing only rotational parts. After formulating an appropriate energy functional, we study the equations of motion and find explicit soliton solutions displaying two-dimensional chiral properties.
MSC:
| 74A35 | Polar materials |
| 74J35 | Solitary waves in solid mechanics |
| 74J30 | Nonlinear waves in solid mechanics |
| 74A30 | Nonsimple materials |
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