this picture is to show how a temporal soliton works. I created the three oscillating impulses with the following gnuplot code. First impulse on left:

set samples 5000
set terminal svg
set output "impulse.svg"
set xrange [-7:7]
set yrange [-1.3:1.3]

set key off
set noxtic
set noytic

set xzeroaxis linewidth 0
set yzeroaxis linewidth 0
#set xtics axis
#set ytics axis

E=2.71

plot E**(-(x**2)/(2*4))*cos(2*pi*x/0.4) with lines linewidth 2

Impulse on the top right:

set samples 5000
set terminal svg
set output "impulse2.svg"

set xrange [-5.5:5.5]
set yrange [-1.3:1.3]

set key off
set noxtic
set noytic

set xzeroaxis linewidth 0
set yzeroaxis linewidth 0
#set xtics axis
#set ytics axis

E=2.71

plot E**(-(x**2)/(2*5))*cos(2*pi*x*(0.008*x**2 -0.09*x + 1)/0.4) with lines linewidth 2

Impulse on the bottom left:

set samples 5000
set terminal svg
set output "impulse3.svg"

set xrange [-7:7]
set yrange [-1.3:1.3]

set key off
set noxtic
set noytic

set xzeroaxis linewidth 0
set yzeroaxis linewidth 0
#set xtics axis
#set ytics axis

E=2.71

plot E**(-(x**2)/(2*4))*cos(2*pi*x*(0.008*x**2 +0.09*x + 1)/0.4) with lines linewidth 2