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Electronic energy-eigen-states of graphene in an orthogonal electromagneticfield with relative magnitude beta=E/vf*B>=1 or in a pure electric field areobtained by a differential-equation method. Gaussian wave packets ofprobability density are constructed and found to transform form two-dimensionalsolitons into one-dimension ones at beta=1, when beta increases form beta<1into beta>1. The maximum number of one-dimensional solitons of a finitegraphene in the field is used to determine the electronic energy levels. Theseenergy levels and the velocity of solitons lead to nonlinear dependence of thecurrent on the Hall voltage for the field with beta>1 and nonlinearcurrent-voltage curves for the pure electric field including the step-like onesat low temperatures, according to the ballistic transport of solitons.

One-dimensional electronic solitons of graphene in an electromagnetic field