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We investigate the effect of the breaking of integrability in the integrals of motion of a sine-Gordon-like system. The class of quasi-integrable models, discussed in the literature, inherits some of the integrable properties they are associated with. Our strategy, to investigate the problem through a deformation of the so-called inverse scattering method, has proven to be useful in the discussion of generic nonlinear Klein-Gordon potentials, as well as in particular cases presented here.
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Palheta et al. (2024) studied this question.
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