  Dispersive shock waves in thermal optical media belong to the third-order
nonlinear phenomena, whose intrinsic irreversibility is described by time
asymmetric quantum mechanics. Recent studies demonstrated that nonlocal wave
breaking evolves in an exponentially decaying dynamics ruled by the reversed
harmonic oscillator, namely, the simplest irreversible quantum system in the
rigged Hilbert spaces. The generalization of this theory to more complex
scenarios is still an open question. In this work, we use a thermal third-order
medium with an unprecedented giant Kerr coefficient, the M-Cresol/Nylon mixed
solution, to access an extremely-nonlinear highly-nonlocal regime and realize
anisotropic shock waves. We prove that a superposition of the Gamow vectors in
an ad hoc rigged Hilbert space describes the nonlinear beam propagation beyond
the shock point. Specifically, the resulting rigged Hilbert space is a
tensorial product between the reversed and the standard harmonic oscillators
spaces. The anisotropy turns out from the interaction of trapping and
antitrapping potentials in perpendicular directions. Our work opens the way to
a complete description of novel intriguing shock phenomena, and those mediated
by extreme nonlinearities.
