We study the nonlinear integrable equation,
u
t
+ 2((
u
x
u
xx
)/
u
) =
ϵu
xxx
, which is invariant under scaling of dependent variable and was called the SIdV equation (see Sen
et al.
2012
Commun. Nonlinear Sci. Numer. Simul
.
17
, 4115–4124 (
doi:10.1016/j.cnsns.2012.03.001
)). The order-
n
kink solution
u
[
n
]
of the SIdV equation, which is associated with the
n
-soliton solution of the Korteweg–de Vries equation, is constructed by using the
n
-fold Darboux transformation (DT) from zero ‘seed’ solution. The kink-type solutions generated by the onefold, twofold and threefold DT are obtained analytically. The key features of these kink-type solutions are studied, namely their trajectories, phase shifts after collision and decomposition into separate single kink solitons.
On a supersymmetric nonlinear integrable equation in (2+1) dimensions