Volume 9, Issue 2 Tricks of the Trade In and Out Download This
Issue Learning about Differential Equations from Their
Symmetries Application of MathSym to Analyzing an Ordinary
Differential Equation In the previous section we used a scaling
symmetry to help understand the solutions of a pair of
differential equations. In each case, the scaling symmetry was
found by inspection. Here I present the computation of the
complete set of point symmetries for two additional differential
equations. Our third example is a nonlinear ordinary
differential that we analyze using its two symmetries. The final
example is the partial differential equation known as the cubic
nonlinear Schrödinger equation . Example three is the ordinary
differential equation that arises in the study of nonlinear
water wave equations. I also show that we can use its two
symmetries to begin to learn something about the structure of
its solutions. MathSym returns a system of equations, the
determining equations, whose solutions generate the symmet