= Schrodinger factorization of the elastic beam equation
{c}
{title2=$u_t=-v_{xx},\quad v_t=u_{xx}$}
Writing $q=u+iv$ in the <free Schrodinger equation> gives $u_t=-v_{xx}$ and $v_t=u_{xx}$, hence $u_{tt}+u_{xxxx}=0$. To encode initial velocity $u_1$, choose the decaying primitive $v_0(x)=-\int_x^\infty(s-x)u_1(s)ds$. A prescribed endpoint curvature becomes the time derivative of the imaginary boundary trace. This turns the normalized <Euler-Bernoulli beam equation> into a complex second-order boundary problem.
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