Scalar-flat Kähler metrics with SU (2) symmetry.
Self-consistent-field method and -functional method on group manifold in soliton theory: a review and new results.
Singularity analysis and integrability of a Burgers-type system of Foursov.
Solitary waves in massive nonlinear -sigma models.
Solitary-wave propagation and interactions for a sixth-order generalized Boussinesq equation.
Soliton and periodic wave solutions to the osmosis equation.
Soliton scattering by delta impurities
Solitons and large time behavior of solutions of a multidimensional integrable equation
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.
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...
Solitons on pseudo-Riemannian manifolds: Stability and motion.
Solitons, peakons, and periodic cuspons of a generalized Degasperis-Procesi equation.
Solutions explosives exceptionnelles
Soluzioni periodiche di PDEs Hamiltoniane
Presentiamo nuovi risultati di esistenza e molteplicità di soluzioni periodiche di piccola ampiezza per equazioni alle derivate parziali Hamiltoniane. Otteniamo soluzioni periodiche di equazioni «completamente risonanti» aventi nonlinearità generali grazie ad una riduzione di tipo Lyapunov-Schmidt variazionale ed usando argomenti di min-max. Per equazioni «non risonanti» dimostriamo l'esistenza di soluzioni periodiche di tipo Birkhoff-Lewis, mediante un'opportuna forma normale di Birkhoff e realizzando...
Solvability of the super KP equation and a generalization of the Birkhoff decomposition.
Some constructive applications of -representations to integration of PDEs
Two new applications of -representations of PDEs are presented: 1. Geometric algorithms for numerical integration of PDEs by constructing planimetric discrete nets on the Lobachevsky plane . 2. Employing -representations for the spectral-evolutionary problem for nonlinear PDEs within the inverse scattering problem method.
Some remarks on the KP system of the Camassa-Holm hierarchy.
Spectral curves, opers and integrable systems
Spectral invariants for coupled spin-oscillators
This text deals with inverse spectral theory in a semiclassical setting. Given a quantum system, the haunting question is “What interesting quantities can be discovered on the spectrum that can help to characterize the system ?” The general framework will be semiclassical analysis, and the issue is to recover the classical dynamics from the quantum spectrum. The coupling of a spin and an oscillator is a fundamental example in physics where some nontrivial explicit calculations can be done.
Spectrum and generation of solutions of the Toda lattice.
Stability and Instability of Solitary Wave Solutions of a Nonlinear Dispersive System of Benjamin-Bona-Mahony Type
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.