24 research outputs found
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 periodic traveling waves for complex modified Korteweg-de Vries equation
We study the existence and stability of periodic traveling-wave solutions for
complex modified Korteweg-de Vries equation. We also discuss the problem of
uniform continuity of the data-solution mapping.Comment: Latex, 20 page
On the stability of the dnoidal waves for the Schr\"odinger-KdV system
We study the periodic Schr\"odinger-Korteweg de Vries system. We describe the
two-parametetric family of periodic traveling waves of dnoidal type. The
main objective of the paper is to establish their spectral stability with
respect to co-periodic perturbations. In the limit , we recover
the results of Albert-Angulo, for the stability of the soliton solutions of
this system on the real line