Small Fluctuations in $λϕ^{n+1}$ Theory in a Finite Domain: An Hirota's Method Approach
We present a method to calculate small stationary fluctuations around static solutions describing bound states in a $(1+1)$-dimensional $λϕ^{n+1}$ theory in a finite domain. We also calculate explicitly fluctuations for the $λϕ^4$. 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 Lamé type Equation and the nonlinear one relies on Hirota's Method.
hep-th↗