  We present a method to calculate small stationary fluctuations around static
solutions describing bound states in a $(1+1)$-dimensional $\lambda \phi^{n+1}$
theory in a finite domain. We also calculate explicitly fluctuations for the
$\lambda \phi^4$. These solutions are written in terms of Jacobi Elliptic
functions and are obtained from both linear and nonlinear equations. For the
linear case we get eingenvalues of a Lam\'e type Equation and the nonlinear one
relies on Hirota's Method.
