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Transverse instability of plane wave soliton solutions of the Novikov-Veselov equation
- Publication Year :
- 2013
-
Abstract
- The Novikov-Veselov (NV) equation is a dispersive (2+1)-dimensional nonlinear evolution equation that generalizes the (1+1)-dimensional Korteweg-deVries (KdV) equation. This paper considers the stability of plane wave soliton solutions of the NV equation to transverse perturbations. To investigate the behavior of the perturbations, a hybrid semi-implicit/spectral numerical scheme was developed, applicable to other nonlinear PDE systems. Numerical simulations of the evolution of transversely perturbed plane wave solutions are presented. In particular, it is established that plane wave soliton solutions are not stable for transverse perturbations.
- Subjects :
- Mathematical Physics
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1304.1489
- Document Type :
- Working Paper