
SIGMA 2 (2006), 078, 12 pages nlin.SI/0512016v2
http://dx.doi.org/10.3842/SIGMA.2006.078
Integrable Hierarchy of Higher Nonlinear Schrödinger Type Equations
Anjan Kundu
Saha Institute of Nuclear Physics, Theory Group &
Centre for Applied Mathematics & Computational Science, 1/AF Bidhan Nagar, Calcutta 700 064, India
Received August 14, 2006, in final form October 17, 2006; Published online November 10, 2006
Abstract
Addition of higher nonlinear terms to the well known
integrable nonlinear Schrödinger (NLS) equations, keeping the same linear dispersion (LD)
usually makes the system nonintegrable. We present a systematic method through a novel
EckhausKundu hierarchy, which can generate higher
nonlinearities in the NLS and derivative NLS equations
preserving their integrability. Moreover,
similar nonlinear integrable extensions can be made again in a
hierarchical way for each of the equations in the known integrable
NLS and derivative NLS hierarchies with higher order LD,
without changing their LD.
Key words:
NLSE & DNLSE; higher nonlinearity; linear dispersion preservation; integrable EckhausKundu hierarchy.
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