  We extend the anholonomic frame and connection deformation method, AFCDM, for
constructing exact and parametric solutions in general relativity, GR, to
geometric flow models and modified gravity theories, MGTs, with nontrivial
torsion and nonmetricity fields. Following abstract geometric or variational
methods, we can derive corresponding systems of nonmetric gravitational and
matter field equations which consist of very sophisticated systems of coupled
nonlinear PDEs. Using nonholonomic frames with dyadic spacetime splitting and
applying the AFCDM, we prove that such systems of PDEs can be decoupled and
integrated in general forms for generic off-diagonal metric structures and
generalized affine connections. We generate new classes of quasi-stationary
solutions (which do not depend on time like coordinates) and study the physical
properties of some physically important examples. Such exact or parametric
solutions are determined by nonmetric solitonic distributions and/or
ellipsoidal deformations of wormhole hole configurations. It is not possible to
describe the thermodynamic properties of such solutions in the framework of the
Bekenstein-Hawking paradigm because such metrics do not involve, in general,
certain horizons, duality, or holographic configurations. Nevertheless, we can
always elaborate on associated Grigori Perelman thermodynamic models elaborated
for nonmetric geometric flows. In explicit form, applying the AFCDM, we
construct and study the physical implications of new classes of traversable
wormhole solutions describing solitonic deformation and dissipation of
non-Riemannian geometric objects. Such models with nontrivial gravitational
off-diagonal vacuum are important for elaborating models of dark energy and
dark matter involving wormhole configurations and solitonic-type structure
formation.
