One-Dimensional Solitary-Wave Solutions in Scalar–Tensor Gravity Coupled to Aharonov–Bohm Electrodynamics

A recently proposed tensor–scalar extension of gravity coupled to extended Aharonov–Bohm electrodynamics admits one-variable traveling reductions in which a longitudinal electromagnetic scalar mode S=∂μAμ couples nonlinearly to gravitational scalars. In the weak-field regime outside sources, a one-dimensional traveling ansatz depending on ξ=x−vt reduces the field equations to a coupled autonomous ODE system. The mathematical core of the reduction is a singular Newton-type equation whose classical mechanics counterpart is known; the novelty here lies in its derivation from the scalar–tensor/Aharonov–Bohm field system, in the physically motivated normalization of the traveling-wave families, and in the resulting phase–space interpretation for source-generated pulse selection. We provide a systematic classification of all admissible initial data and of the corresponding maximal solutions, distinguishing repulsive/attractive regimes and subcritical/critical/supercritical behaviors through a normalized parameter map. In particular, attractive branches may reach the singularity in finite time with a universal collision exponent 2/3, while escaping branches exhibit asymptotically uniform motion with a computable logarithmic correction. Finally, we construct a numerical atlas of representative trajectories and validate the computations by cross-checking direct time integration against numerical inversion of the implicit quadrature, together with energy-defect diagnostics.