Integrable Hierarchy of Higher Nonlinear Schrödinger Type Equations

Details Integrable Hierarchy of Higher Nonlinear Schrödinger Type Equations Integrable Hierarchy of Higher Nonlinear Schrödinger Type Equations

2005-12-08

arxiv.org/abs/nlin/0512016v3

SIGMA 2 (2006), 078, 12 pages

Nonlinear Sciences

Exactly Solvable and Integrable Systems

Published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/

Scientific paper

10.3842/SIGMA.2006.078

Addition of higher nonlinear terms to the well known integrable nonlinear Schr\"odinger (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.

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