Geodesic
Integrable Hierarchy of Higher Nonlinear Schrödinger Type Equations
Symmetry, integrability and geometry: methods and applications, Tome 2 (2006)

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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. 
Anjan Kundu. Integrable Hierarchy of Higher Nonlinear Schrödinger Type Equations. Symmetry, integrability and geometry: methods and applications, Tome 2 (2006). http://geodesic.mathdoc.fr/item/SIGMA_2006_2_a77/
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