This article is cited in 19 papers

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

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.

Keywords: NLSE & DNLSE; higher nonlinearity; linear dispersion preservation; integrable Eckhaus–Kundu hierarchy.

MSC: 35G20; 37C85; 35G25; 37E99

Received: August 14, 2006; in final form October 17, 2006; Published online November 10, 2006

Language: English

DOI: 10.3842/SIGMA.2006.078

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ArXiv: nlin.SI/0512016v2