In this work, we explore the bright soliton solutions of a non-local variant of the complex modified Korteweg–de Vries (cmKdV) equation, characterised by shifted reverse space–time \(\mathcal{P}\mathcal{T}\) -symmetry. Employing the bilinear method and \(\tau \) -functions of KP hierarchy, we obtain exact solutions in determinant representation that inherently preserve the symmetry structure of the equation. A detailed analysis of the one-soliton case reveals a distinct inverse relationship between soliton velocity and amplitude, and notably, the amplitude can diverge to infinity through the adjustment of a velocity-independent parameter, unlike in the local cmKdV case. For multi-soliton solutions, we perform a long-time asymptotic analysis, showing that the solutions decompose into superpositions of individual bright solitons. Furthermore, we rigorously examine their interaction dynamics, confirming that the collisions are purely elastic and accompanied by quantifiable phase shifts and positional displacements. The findings shed new light on the rich and previously unexplored interaction behaviur of solitons in this class of non-local integrable models.
