Solitons of the square-rectangular martensitic transformation

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Abstract
The static solitons of the square-rectangular martensitic transformation are obtained with the use of higher-order elasticity theory; both first-order (rectangular-rectangular and square-rectangular solitons) and second-order (rectangular-rectangular only) phase transitions are treated. The shear and dilatational strains vanish in all cases. The deviatoric strains are calculated exactly, and the displacement vectors are obtained as power series, using the full (nonlinear) Lagrangian strain tensor. In the first-order case, the width of the rectangular-rectangular soliton diverges as the transition temperature is approached from below; the soliton splits gradually into two square-rectangular solitons, both of finite width, whose separation diverges at the transition temperature.