
22.2. Analytical Solutions and Their Visualizations 1287
with Maple results
Sol1 := u(x, y, z,t) = C9
tanh
−
p
C2
2
+ C3
2
+ C4
2
ct + C2x + C3 y + C4 z + C1
3
+ C7 tanh
−
p
C2
2
+ C3
2
+ C4
2
ct + C2x + C3y + C4 z + C1
+ C6
In ge neral, hyperbolic linear PDEs can have interesting traveling wave solutions. However, for
nonlinear equations the effects of nonlinear and higher-order terms interact a nd can lead to interest-
ing solutions [see Shingareva and Liz´arraga-Celaya (2011), Shingareva and Liz´arraga-Celaya (pp.
1622–1765, 2012)]. By applying the function
TWSolutions
(with various options) of the package
PDEtools
, one can construct various types of traveling