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Solitons and large time behavior of solutions of a multidimensional integrable equation

Anna Kazeykina (2013)

Journées Équations aux dérivées partielles

Novikov-Veselov equation is a (2+1)-dimensional analog of the classic Korteweg-de Vries equation integrable via the inverse scattering translform for the 2-dimensional stationary Schrödinger equation. In this talk we present some recent results on existence and absence of algebraically localized solitons for the Novikov-Veselov equation as well as some results on the large time behavior of the “inverse scattering solutions” for this equation.

Solitons of the sine-Gordon equation coming in clusters.

Cornelia Schiebold (2002)

Revista Matemática Complutense

In the present paper, we construct a particular class of solutions of the sine-Gordon equation, which is the exact analogue of the so-called negatons, a solution class of the Korteweg-de Vries equation discussed by Matveev [17] and Rasinariu et al. [21]. Their characteristic properties are: Each solution consists of a finite number of clusters. Roughly speaking, in such a cluster solitons are grouped around a center, and the distance between two of them grows logarithmically. The clusters themselves...

Some constructive applications of Λ 2 -representations to integration of PDEs

A. Popov, S. Zadadaev (2000)

Annales Polonici Mathematici

Two new applications of Λ 2 -representations of PDEs are presented: 1. Geometric algorithms for numerical integration of PDEs by constructing planimetric discrete nets on the Lobachevsky plane Λ 2 . 2. Employing Λ 2 -representations for the spectral-evolutionary problem for nonlinear PDEs within the inverse scattering problem method.

Stability and Instability of Solitary Wave Solutions of a Nonlinear Dispersive System of Benjamin-Bona-Mahony Type

Hakkaev, Sevdzhan (2003)

Serdica Mathematical Journal

2000 Mathematics Subject Classification: 35B35, 35B40, 35Q35, 76B25, 76E30.This paper concerns the orbital stability and instability of solitary waves of the system of coupling equations of Benjamin-Bona-Mahony type. By applying the abstract results of Grillakis, Shatah and Strauss and detailed spectral analysis, we obtain the existence and stability of the solitary waves.Partially Supported by Grant MM-810/98 of MESC and by Scientefic Research Grant 19/12.03.2003 of Shumen University.

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