Since the rate of amplitude damping in both NDB compactons and the KdV solitons are similar, one can intuitively interpret this behavior as a transformation of a NDB compacton into a KdV soliton during its propagation.
[39.] Tanaka, M., "Perturbations on the KdV solitons an approach based on the multiple time scale expansion," J.
On the
KdV soliton formation and discrete spectral analysis.
Reporting on their joint research, Ricketts (Carnegie Mellon U., Pennsylvania) and Ham (Harvard University, Massachusetts) offer a comprehensive treatment of the
KdV soliton on the nonlinear transmission line; they are not concerned here with solitons in other media or with other kinds of solitons in the electrical domain.
The first solution type is a single KdV soliton, i.e., just a single KdV soliton emerges over time.
The second solution type is a KdV soliton ensemble.
Figure 2(b) shows the dependence of the pulse width of a single KdV soliton on [V.sub.b], calculated by Eq.
As a result, both the c- and [pi]-modes are known to support the KdV solitons [11].
The localized initial wave [(3:1).sub.2] is the analytical solution for equation (2.9) in the case of w = 0, i.e., it represents the
KdV soliton.
On the other hand, numerical simulations demonstrate that for some initial conditions a train of KdV2 solitons, almost the same as that of
KdV solitons, emerges from the cosine wave as in Zabusky and Kruskal [8] numerical simulation.
The striking pattern of soliton trajectories emerging for the
KdV solitons is described by Salupere et al.