Analysis of Soliton Solutions for the Real Nonlocal Modified Korteweg–de Vries Equation

In this paper, we investigate the real reverse-space–time nonlocal modified Korteweg–de Vries equation using the ∂¯-dressing representation established by Luo and Fan. By specializing the purely imaginary discrete spectral data, we obtain explicit one-, two- and three-soliton expressions from the general determinant formula. We then examine their profiles and parameter-dependent evolution. For regular one-soliton branches, the characteristic velocity and exponential amplitude rate are derived analytically. Depending on the spectral parameters, the amplitude may grow in one temporal direction and attenuate in the reverse direction, while the solution remains spatially localized at each finite time. The nonlocal product q(x,t)q(−x,−t) is shown to be invariant under joint space–time reflection, highlighting the dynamical role of the reverse-space–time coupling and its difference from the real local mKdV equation.