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We construct analytical periodic wave and soliton solutions to the generalized nonautonomous nonlinear Schrodinger equation with time- and space-dependent distributed coefficients in harmonic and optical lattice potentials. We utilize the similarity transformation technique to obtain these solutions. Constraints for the dispersion coefficient, the nonlinearity, and the gain (loss) coefficient are presented at the same time. Various shapes of periodic wave and soliton solutions are studied analytically and physically. Stability analysis of the solutions is discussed numerically.

Based on Dyson–Schwinger Equations (DSEs) in the ``rainbow" approximation, the dependence of quark effective mass on gluon propagator is investigated by use of three different phenomenological gluon propagators with two parameters, the strength parameter χ and range parameter Δ. Our theoretical calculations for the quark effective mass Mf(p2), defined by the self-energy functions Af(p2) and Bf(p2) of the DSEs, show that the dynamically running quark effective mass is strongly dependent on gluon propagator. Therefore, because gluon propagator is completely unknown, the quark effective mass cannot be exactly determined theoretically.

Based on the Pomeron exchange model, elastic production of meson in electron-proton interaction is investigated with both linear and non-linear Pomeron trajectories. The numerical calculations of the differential cross section for e + p → e' + p + are performed. The theoretical predictions show that the dependence of the differential cross section on virtual photon virtuality, Q2, is of moderation, the change of the energy scale parameter s0 causes moderate effect on the differential cross section, and the linear trajectory is a good approximation to non-linearity of the Pomeron trajectory, in particular, at small momentum transfer region t ≤ 0.2 GeV2.