A New Type of Nonlinear Plasma Equation. II. Annihilative and Transparent Interactions of Pulses

Abstract

In part II we give some analytical properties and numerical solutions of the nonlinear equation which was derived in the companion paper (part I). As a result of numerical calculations, a new phenomenon is discovered, namely, that a positive pulse and a negative pulse placed separately begin to move in the direction toward each other and annihilate on collision. On the other hand, when only a positive (or negative) disturbance is imposed, it disintegrates into several pulses of the form cos²x, each pulse running in the same direction with a speed proportional to its amplitude, so that a bigger pulse passes through a smaller one without changing the shape, as the KdV solitons do. When they get together, the amplitude of the combined pulse becomes smaller than the bigger one but the width becomes wider.