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Spectral stability of special discontinuities. (English. Russian original) Zbl 1326.35316
Dokl. Math. 91, No. 3, 347-351 (2015); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 462, No. 5, 512-516 (2015).
This paper analyzes the (linear) stability of the structure of special discontinuities corresponding to the solution of generalized KdV-Burgers equation. A discontinuity is called special if its structure represents a heteroclinic phase curve joining two saddle-type special points (of which one is the state ahead of the discontinuity and the other is the state behind the discontinuity). It is proved that only one special discontinuity with a monotone structure is stable. Special discontinuities with a nonmonotone structure are unstable.

MSC:
35Q53 KdV equations (Korteweg-de Vries equations)
35B35 Stability in context of PDEs
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