NLSE for quantum plasmas with the radiation damping

We consider contribution of the radiation damping in the quantum hydrodynamic equations for spinless particles. We discuss possibility of obtaining of corresponding non-linear Schrodinger equation (NLSE) for the macroscopic wave function. We compare contribution of the radiation damping with weakly (or semi-) relativistic effects appearing in the second order by v/c. The radiation damping appears in the third order by v/c. So it might be smaller than weakly relativistic effects, but it gives damping of the Langmuir waves which can be considerable.

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