Small Fluctuations in $λϕ^{n+1}$ Theory in a Finite Domain: An Hirota's Method Approach

Gama, M. C.; Carrillo, J. A. Espichán; Maia Jr, A.

Small Fluctuations in $λϕ^{n+1}$ Theory in a Finite Domain: An Hirota's Method Approach

Authors

Gama, M. C.

Carrillo, J. A. Espichán

Maia Jr, A.

Description

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.
10 pages