This paper offers an in-depth investigation into the bright soliton solutions on periodic backgrounds to the nonlocal Davey–Stewartson I equation with fully space-shifted PT\documentclass[12pt]{minimal}
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\begin{document}$$\mathcal{P}\mathcal{T}$$\end{document}-symmetry. These exact solutions, derived using the bilinear method, embody the coherent structure of bright solitons and specific time-independent periodic waves. Through extensive examinations of the long-time behaviors of the bright solitons on periodic backgrounds, their interaction scenarios are further explored. Of particular interest is the periodic behavior exhibited by the amplitudes of bright solitons concerning the two spatial variables x and y. In two distinct parameter limit cases, the specific time-independent periodic waves degenerate to the zero plane wave, and the periodicity of soliton amplitudes vanishes, resulting in fixed values as x→±∞\documentclass[12pt]{minimal}
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\begin{document}$$x\rightarrow \pm \infty $$\end{document} or y→±∞\documentclass[12pt]{minimal}
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\begin{document}$$y\rightarrow \pm \infty $$\end{document}. Particularly, under these two special limits, significant alterations occur in the soliton amplitudes, fundamentally distinguishing them from the property of unaltered soliton amplitudes during bright soliton interactions in the case of zero background.
