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Integrable Hierarchy of Higher Nonlinear Schrödinger Type Equations

Anjan Kundu
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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.

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Anjan Kundu. 2006-11-13. Integrable Hierarchy of Higher Nonlinear Schrödinger Type Equations. https://doi.org/10.3842/sigma.2006.078

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