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

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

2008-07-02

arxiv.org/abs/0807.0269v1

Physics

High Energy Physics

High Energy Physics - Theory

10 pages

Scientific paper

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.

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