Stability of periodic solutions to nonlinear Klein-Gordon equations
We study the stability of periodic travelling wave solutions to nonlinear Klein-Gordon equations, subject to small and localized perturbations. Using the periodic Evans function technique, we analyze the spectrum of a linearized quadratic eigenvalue pencil associated with the linearized equation, in a neighbourhood of the origin on the spectral plane. The stability criterion is expressed in terms of signature of an index involving physical parameters of the wave, thereby holding the result valid for a general nonlinearity F(u). The result is then verified for the following cases: • cubic nonlinearity; F(u) = u3 − u • sine Gordon equation; F(u) = − sin(u)
nonlinear klein gordon equation, modulational instability, periodic solutions, evans function, stability index
University of Illinois - Urbana-Champaign
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University of Illinois at Urbana-Champaign