File:Soliton 2nd order.svg

the plot of a 2nd order soliton. It's the 2D plot of the modulus of the following function:

${\displaystyle a(\xi ,\zeta )={\frac {4[\cosh(3\xi )+3e^{4i\zeta }\cosh(\xi )]e^{i\zeta /2}}{\cosh(4\xi )+4\cosh(2\xi )+3\cos(4\xi )}}}$

I made it with the following Gnuplot code:

set terminal svg
set output "Soliton_2nd_order.svg"

# choose quality
set samples 50, 50
set isosamples 70

# change the angle the plot is shown
set view 55, 45, 1, 2

# output of the surface
set pm3d at bs
set hidden3d offset 1 trianglepattern 3 undefined 1 altdiagonal bentover
set style data lines

# remove the box with the meaning of the color
unset colorbox

# set ranges
set xrange [-1.5:1.5]
set yrange [0:pi]
set zrange [0:1]


set grid
set key off

# remove tics on the z-axis
unset ztics


set xlabel "xi"
set ylabel "zeta"

#set xzeroaxis linetype -1 linewidth 0.5
#set yzeroaxis linetype -1 linewidth 0.5
set xtics axis
set ytics axis


I=sqrt(-1)

splot abs((cosh(3*x) + 3*exp(4*I*y)*cosh(x))/(cosh(4*x) + 4*cosh(2*x) + 3*cos(4*y)))