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Structural stability of the Korteweg-de Vries solitons under a singular perturbation. (English) Zbl 0695.35161

Summary: We investigate the stability of a solitary wave solution of the Korteweg- de Vries equation \[ \delta^ 2u_{5x}+u_{3x}+6uu_ x+u_ t=0, \] when a fifth order spatial derivative term is added. We show that the solution ceases to be strictly localized but develops an infinite oscillating tail and we compute the amplitude of the latter.

MSC:

35Q99 Partial differential equations of mathematical physics and other areas of application
35B35 Stability in context of PDEs
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