Recent content by Lenore

If a non-trivial solution that fits the boundary conditions X(+/-infty)=0, X(x)=X(-x) cannot be provided in this way, does this mean that the solution simply cannot be given in terms of elementary functions or that no separable solution exists for the original PDE? Very grateful.

From the two linearly independent solutions (exp(-ax), exp(ax)) I retain only the one with the negative exponent, because the positive one blows up at infty and patch the other one up by letting y->|y|, so that both the boundary conditions at +/-infty and the evenness of the solution are...

As part of a separable solution to a PDE, I get the following ODE: X''-rX=0 (*), with -infty<x<infty and the boundary condition X(+/-infty)=0 (X is an odd function here). Thus I have assumed r>0 to avoid the periodic solution, cos. I, therefore, argue that the solution is the symmetric...