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Schr\"{o}dinger field theory with an attractive self-interaction possessnon-topological extended solutions with a finite energy in both finite andinfinite-volume cases, namely, bright solitons. The analytical form of thesolution itself is well-known, though analytical investigation of the quantumfluctuations in this background still requires more thorough investigation, forinstance, analytical computation of quantum corrections to this backgroundwithin the saddle-point approximation. In the present work this gap is filled.Both 2-point Green's function and quantum corrections to the background areanalytically computed and properly renormalized by means of momentum cut-offprocedure. It is deduced that quantum corrections are indeed small providedthat particle number is large. Also, we see that perturbation modes ofcontinuum spectrum at bright soliton background generate a gap in the energyspectrum. Moreover, it turns out that the whole spectrum is continuous modulozero-modes, which is similar to Sine-Gordon solitons.

Analytical computation of quantum corrections to non-topological soliton (bright soliton) within the saddle-point approximation