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The non-commutative strategy developed by Bagarello (see Int. Jour. ofTheoretical Physics, 43, issue 12 (2004), p. 2371 - 2394) for the analysis ofsystems of ordinary differential equations (ODEs) is extended to a class ofpartial differential equations (PDEs), namely evolution equations andNavier-Stokes equations. Systems of PDEs are solved using an unboundedself-adjoint, densely defined, Hamiltonian operator and a recursion relationwhich provides a multiple commutator and a power series solution. Numerousexamples are given in this work.

Generalizing Bagarello's operator approach to solve a class of partial differential equations