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The Boussinesq equation is known to be the fundamental nonlinear model, describing wave propagation in a weakly dispersive nonlinear medium. In this paper, we prove the existence of the collapse dynamics for the two basic forms of the Boussinesq equation in the case of the periodic boundary conditions. The sufficient criterion of the blow-up is found analytically.
Sergei K. Turitsyn (Mon,) studied this question.
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