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The spectrum of travelling wave solutions to the Sine-Gordon equation

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  • We investigate the spectrum of the linear operator coming from the sine-Gordon equation linearized about a travelling kink-wave solution. Using various geometric techniques as well as some elementary methods from ODE theory, we find that the point spectrum of such an operator is purely imaginary provided the wave speed $c$ of the travelling wave is not $\pm 1$. We then compute the essential spectrum of the same operator.
    Mathematics Subject Classification: Primary: 35P30, 74J30 Secondary: 35P05.


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