Stability of solitary-wave pulses in shape-memory alloys

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Abstract
Within the framework of a one-dimensional continuous Ginzburg-Landau theory, pulselike solitary waves in shape-memory alloys are investigated. By neglecting heat conduction, internal friction, and external volume forces, but including shear-strain and strain-gradient contributions in addition to the Landau internal energy, a simple equation of motion is derived for the displacement of the atomic planes. It is shown that it has pulselike solitary-wave solutions for both the austenitic and the martensitic phase. The stability of the solitary pulses is investigated by the Liapunov method. Stability functionals are presented and analyzed. In the parameter regions where they do not satisfy the Liapunov criteria for stability, instability can be proved by variational methods. Thus, necessary and sufficient stability criteria are available for the existing pulselike solitary waves in shape-memory alloys. The criteria and their physical consequences are discussed.