The Boussinesq equation revisited

The continuous spectrum and soliton solutions for the Boussinesq equation are investigated using the ∂-dressing method. Solitons demonstrate quite extraordinary behavior; they may decay or form a singularity in a finite time. Formation of singularity (collapse of solitons) for the Boussinesq equation was discovered several years ago. Systematic study of the solitonic sector is presented.

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