Singular Asymptotic Expansions and Delta Waves for Burger's Equation.
Smoothing of dispersive waves
Solitary wave solutions for a time-fraction generalized Hirota-Satsuma coupled KdV equation by a new analytical technique.
Solitary waves of generalized Kadomtsev-Petviashvili equations
Soliton and periodic wave solutions to the osmosis equation.
Soliton dynamics for the Korteweg-de Vries equation with multiplicative homogeneous noise.
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...
Solutions classification to the extended reduced Ostrovsky equation.
Solving the systems of equations arising in the discretization of some nonlinear p.d.e.'s by implicit Runge-Kutta methods
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 properties of solutions for the generalized thin film equation in one space dimension.
Some relatively new techniques for nonlinear problems.
Some remarks on the KP system of the Camassa-Holm hierarchy.
Space of local fields in integrable field theory and deformed abelian differentials.
Spatial analyticity of solutions of a nonlocal perturbation of the KdV equation.
Spectral analysis of long wavelength periodic waves and applications.
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.
Stability of multipeakons