Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 2 (2006), 078, 12 pages      nlin.SI/0512016v2      https://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 Eckhaus-Kundu 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 Eckhaus-Kundu hierarchy.

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