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Journal of Science and Technology in the Tropics 35
RESULTS AND DISCUSSION
Equation (19) gives the renormalized KdV soliton whose amplitude and widths
are given by Eqs. (20) and (21), respectively. Equation (26) represents the higher
order correction to KdV soliton whose speed is λ + δλ and amplitude and width
are given by Eqs. (31) and (32). The solutions of Eqs. (16) and (17) are obtained by
the method of renormalization [38]. Although several investigators ([32-35]) have
used the method of variation of parameters to find the particular solution of the
higher order correction, we chose a simpler technique by considering the particular
solution as a truncated power series of [36].
The dust acoustic dressed soliton in four component plasma with superthermal
electron is considered. The effects of higher order nonlinear terms on solitons are
illustrated by plotting the KdV soliton (dotted line),
the higher order correction
(dashed line) and the dressed soliton (solid line) vsη as shown in Figure 1(a).
The other parameters are λ = 0.3 , m
i
= 0.5 , m
e
= 0.5 , σ = 0.15 , α = 1, β = 1, and
κ = 1.5 . It is seen that the amplitude of the higher order correction (dashed line)
is smaller than the the amplitude of KdV soliton (dotted line). The dressed soliton
(solid line) vs η for κ = 1000 is as shown in Figure 1(b). The other parameters
are same as in Figure 1(a). The amplitude of the dressed soliton (solid line) is
found to be larger than the amplitude of the KdV soliton (dotted line) . Also the
amplitude of KdV soliton is larger than the amplitude of higher order correction
(dashed line). From the perturbation theory it is known that one can only consider
the higher order correction if
. On the contrary, non-physical
solution is obtained if
. So Figure 1(a) and (b) are physical.
Figure 1. The KdV soliton (dotted line) ψ
the dressed soliton (solid line)ψ are plotted against
η . Top: 1(a) κ = 1.5 , λ = 0.3 , m
i
= 0.5 , m
e
= 0.5 , σ = 0.15 ,
α = 1 and β = 1. Bottom: 1(b) κ = 1000 , λ = 0.3 , m
i
= 0.5 ,
m = 0.5 , σ = 0.15 , α = 1 and β = 1.
e
(1)
(2)
, the higher order correction (dashed line) ψ and