One-soliton (we plot w = -u against x, for various t) from p. 74 of Drazin and Johnson, ``Solitons,

an Introduction'', Cambridge Texts in Applied Mathematics, 1989.

> w1 := 2*sech(x-4*t)^2;

w1 := 2*sech(x-4*t)^2

> with(plots):

Warning, the name changecoords has been redefined

> animate( w1, x=-20..20, t=-5..5, frames=50 , numpoints=101,
colour=BLACK, axes=BOXED,thickness=3);

[Maple Plot]

Two-soliton solution, from p. 75

> w2 := 12*(3+4*cosh(2*x-8*t)+cosh(4*x-64*t))/(3*cosh(x-28*t)+cosh(3*x-36*t))^2;

w2 := 12*(3+4*cosh(2*x-8*t)+cosh(4*x-64*t))/((3*cos...

> animate( w2, x=-3..3, t=-1..1, frames=50, numpoints=101 , colour=black,thickness=3,
axes=BOXED);

[Maple Plot]