In this work, we explore a massless nonlinear Dirac equation, i.e., a nonlinear Weyl equation. We study the dynamics of its pulse solutions and find that a localized one-hump initial condition splits into a localized two-hump pulse, while an associated phase structure emerges in suitable components of the spinor field. For times larger than a transient time t_{s} this pulse moves with the speed of light, effectively featuring linear wave dynamics and maintaining its shape (both in two and three dimensions). We show that for the considered nonlinearity, this pulse represents an exact solution of the nonlinear equation. Finally, we briefly comment on the generalization of the results to a broader class of nonlinearities.
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Article Synopsis
- * By manipulating the Dirac mass, researchers have created techniques for engineering band structures and confining electrons, including the formation of Jackiw-Rebbi-type Dirac boundary modes at domain walls.
- * This study demonstrates that nonlinearity in a 1D Dirac material can create a self-induced domain boundary, allowing for significant changes in conductivity when the material is pushed past a certain threshold.
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