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We prove integrability of a generalised non-commutative fourth order quinticnonlinear Schrodinger equation. The proof is relatively succinct and rooted inthe linearisation method pioneered by Ch. Poppe. It is based on solving thecorresponding linearised partial differential system to generate anevolutionary Hankel operator for the `scattering data'. The time-evolutionarysolution to the non-commutative nonlinear partial differential system is thengenerated by solving a linear Fredholm equation which corresponds to theMarchenko equation. The integrability of reverse space-time and reverse timenonlocal versions, in the sense of Ablowitz and Musslimani, of the fourth orderquintic nonlinear Schrodinger equation are proved contiguously by the approachadopted. Further, we implement a numerical integration scheme based on theanalytical approach above which involves solving the linearised partialdifferential system followed by numerically solving the linear Fredholmequation to generate the solution at any given time.

Integrability of local and nonlocal non-commutative fourth order quintic nonlinear Schrodinger equations