Modified KdV solitons with non-zero vacuum parameter obtainable from the ZS-AKNS inverse method

Abstract

The authors obtain a new N-soliton solution to the modified KdV equation with non-zero vacuum parameter b using the inverse scattering method (see Zakharov and Shabat, 1972 and Ablowitz et al., 1973) under a non-vanishing condition (Kawata and Inoue, 1977). As demonstrations, they study the special features of the one-soliton and two-solitons in detail. The amplitude, width, and magnitude of the velocity of these solitons are all dependent on b. They all move in the positive direction-such a characteristic is different from that of the KdV solitons.