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D.E. Pelinovsky and C. Sulem

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Embedded solitons of the DSII equation

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CRM Proceedings and Lecture Notes, 27,
edited by I.M. Sigal and C. Sulem, 135-145 (2001)

**Abstract:**

We study the stability of exact standing wave solutions in
the focussing Davey--Stewartson II equation. The standing
wave solutions correspond to embedded solitons coupled to
a linear wave spectrum. Decay of localized waves and
propagation of nonlocalized (one-dimensional) solitons is
observed due to instability of the exact solutions with
respect to variations of the initial data. An outline of
the proof of instability of embedded solitons in integrable
PDEs is given for the case study.

**Keywords**:

DAVEY-STEWARTSON II EQUATION, LUMP SOLUTIONS,
EMBEDDED SOLITONS, EMBEDDED EIGENVALUES,
DIRAC OPERATORS, PERTURBATION THEORY FOR LINEAR OPERATORS