In the experiments on tangential fuel pellet injection in the TUMAN-3M tokamak an initiation of LH-transition or, in several scenarios-temporal (1-2 ms) confinement improvement with the following backwards transition was observed. To understand the possibility of the transitions, a model calculating the evolution of density and ion temperature profiles under the effect of source profile perturbation and plasma cooling created by pellet evaporation was developed. In the model, a diffusion coefficient depending on radial electric field shear value was used. Turbulence parameters are defined using a gyrokinetic simulation of the experiments with ELMFIRE code. Modeling results are in good agreement with experiments. Using the data obtained from the modeling, non-linear particle flux dependency on density gradient was analyzed; the existence of two stabile solutions for two confinement modes dependent on particle flux value was proved, in agreement with experiments.