On spectral stability of solitary waves of nonlinear Dirac equation on a line

Details On spectral stability of solitary waves of nonlinear Dirac equation on a line On spectral stability of solitary waves of nonlinear Dirac equation on a line

2009-10-06

arxiv.org/abs/0910.0917v5

Physics

Mathematical Physics

16 pages with figures. Added/corrected references

Scientific paper

We consider the nonlinear Dirac equation in one dimension (the massive Gross-Neveu model). We explicitly construct solitary wave solutions, and then study the linearization of the equation at a solitary wave. We present numerical simulations and justify them with explicit construction of some of the eigenfunctions. Then we present a WKB-based argument which justifies (but does not prove) the spectral stability of solitary waves of sufficiently small amplitude. We also compare our results with previously known numerical simulations.

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