## Journals

- Advances in Mathematics of Communications
- Big Data & Information Analytics
- Communications on Pure & Applied Analysis
- Discrete & Continuous Dynamical Systems - A
- Discrete & Continuous Dynamical Systems - B
- Discrete & Continuous Dynamical Systems - S
- Evolution Equations & Control Theory
- Inverse Problems & Imaging
- Journal of Computational Dynamics
- Journal of Dynamics & Games
- Journal of Geometric Mechanics
- Journal of Industrial & Management Optimization
- Journal of Modern Dynamics
- Kinetic & Related Models
- Mathematical Biosciences & Engineering
- Mathematical Control & Related Fields
- Mathematical Foundations of Computing
- Networks & Heterogeneous Media
- Numerical Algebra, Control & Optimization
- AIMS Mathematics
- Conference Publications
- Electronic Research Announcements
- Mathematics in Engineering

### Open Access Journals

DCDS

Going back to considerations of Benjamin (1974), there has been
significant interest in the question of stability for the stationary
periodic solutions of the Korteweg-deVries equation, the so-called
cnoidal waves. In this paper, we exploit the squared-eigenfunction
connection between the linear stability problem and the Lax pair for
the Korteweg-deVries equation to completely determine the spectrum
of the linear stability problem for perturbations that are bounded
on the real line. We find that this spectrum is confined to the
imaginary axis, leading to the conclusion of spectral stability. An
additional argument allows us to conclude the completeness of the
associated eigenfunctions.

DCDS

A new method due to Fokas for explicitly solving boundary-value problems for linear partial differential equations is extended to equations with mixed partial derivatives. The Benjamin-Bona-Mahony equation is used as an example: we consider the Robin problem for this equation posed both on the half line and on the finite interval. For specific cases of the Robin boundary conditions the boundary-value problem is found to be ill posed.

## Year of publication

## Related Authors

## Related Keywords

[Back to Top]