BPS and Semi-BPS Kink Families in N-Component Scalar Field Theories with Fourth-Degree Polynomial Potentials
DOI:
https://doi.org/10.66972/iscis21202623Keywords:
Topological Solitons, Kink Families, Bogomolny Formalism, Multi-Component Scalar Fields, Poschl-Teller Spectrum, Physics-Informed Neural NetworksAbstract
We develop a constructive theory of kink solutions in N-component scalar field theories in (1+1) dimensions whose self-interactions are at most quartic and which carry a discrete symmetry. Working inside the Bogomolny first-order framework, we build the potentials from superpotentials and classify the models that support continuous families of BPS and semi-BPS kinks. The two-component MSTB and BNRT systems, together with the recently introduced single-singular-point models, reappear as the N=2 slice of a much larger landscape. The central result is a fully explicit one-parameter family of N-component quartic potentials for which we determine the 2N vacua, the first-order semi-BPS equations, the embedded one-component kinks, the exact energy sum rules, and the closed-form transverse Poschl-Teller spectra. The composite defects are interpreted through exact energy budgets. Because the generic profiles are not elementary, we show that a physics-informed neural network integrates the first-order equations directly and comment on multi-field solitons in the life sciences.
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