S. Cui and D.E. Pelinovsky
Stability of standing periodic waves in the massive Thirring model
Studies in Applied Mathematics 154 (2025) e12789 (24 pages)
Abstract:
We analyze the spectral stability of the standing periodic waves in the massive Thirring model in laboratory coordinates. Since
solutions of the linearized MTM equation are related to the squared eigenfunctions of the linear Lax system, the spectral stability
of the standing periodic waves can be studied by using their Lax spectrum. We show analytically that each family of standing
periodic waves is distinguished by the location of eight eigenvalues which coincide with the end points of the spectral bands of
the Lax spectrum. The standing periodic waves are proven to be spectrally stable if the eight eigenvalues are located either on
the imaginary axis or along the diagonals of the complex plane. By computing the Lax spectrum numerically, we show that this
stability criterion is satisfied for some standing periodic waves.
Keywords:
massive Thirring model, standing periodic waves, spectral stability, squared
eigenfunctions, Lax spectrum