Skip to Main Content
Handbook of Linear Partial Differential Equations for Engineers and Scientists, 2nd Edition
book

Handbook of Linear Partial Differential Equations for Engineers and Scientists, 2nd Edition

by Andrei D. Polyanin, Vladimir E. Nazaikinskii
December 2015
Intermediate to advanced content levelIntermediate to advanced
1643 pages
59h 33m
English
Chapman and Hall/CRC
Content preview from Handbook of Linear Partial Differential Equations for Engineers and Scientists, 2nd Edition
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
Become an O’Reilly member and get unlimited access to this title plus top books and audiobooks from O’Reilly and nearly 200 top publishers, thousands of courses curated by job role, 150+ live events each month,
and much more.
Start your free trial

You might also like

Differential Equations, 2nd Edition

Differential Equations, 2nd Edition

Steven G. Krantz

Publisher Resources

ISBN: 9781466581494