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Spinors and Twistors in the Description of Rotational Seismic Waves and Spin and Twist Solitons

Institute of Geophysics, Polish Academy of Sciences, ul. Ksicia Janusza 64, 01-452 Warsaw, Poland emaj{at}igf.edu.pl

A noncommutative (anti-) self-dual Yang–Mills theory as a source of multisoliton solutions of nonlinear wave equations was applied to the description of rotational seismic waves that are excited in the earthquake source. Spinors and twistors are used to describe spin and twist solitons branching off dispersion curves for rotational seismic waves. Complex physical structures are adopted to describe spin and twist effects resulting from the presence of translational and rotational defects in elastic rocks. A seismic space is also assumed to have a complex structure. An earthquake source zone is modeled by a set of equations for interacting fields that is mathematically similar to the noncommutative (anti-) self-dual Yang–Mills equations. Some similarities between dislocations and strings are emphasized, for example, those that exist between surface defects and D-branes in string theories. Dislocations and disclinations are treated as sources for seismic spin and twist fields. By symmetry reduction various soliton equations for seismic spin and twist solitons can be obtained from the set of earthquake source zone equations, which is similar to the noncommutative (anti-) self-dual Yang–Mills equations by symmetry reduction.

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