  Identification of crack positions or anomalies in materials using the time
reversal based nonlinear elastic wave spectroscopy (TR-NEWS) is an established
method. We propose a system using transducers which emit forward propagating
solitonic wave and time-reversed propagating solitonic wave produced by
memristers placed on a side of a rectangle and scattered by cracks in the
material and received by receivers which are placed on the opposite side of the
rectangle.
  By minimizing the difference of the scattered forward propagating wave and
the scattered TR wave, we get information of the position of the crack by using
the neural network technique. Route of the solitons are expressed by 2
dimensional projective quaternion functions, and parameters for getting the
optimal route from signals are expected to be reduced.
  We consider the wave is expressed by a soliton which is conformal, and
discuss symmetry protected topological impurities and gravitational effects
using the Atiyah-Patodi-Singer's index theorem.
