Information-theoretic measures for a solitonic profile mass Schrödinger equation with a squared hyperbolic cosecant potential

•Solutions to solitonic profile mass Schrödinger equation with squared hyperbolic cosecant potentials are obtained.•Such a study might be interesting to those experimental physicists in condensed matter physics.•The position entropy is calculated considering the singular point.•The complicated Fourier transforms are derived.•BBM inequality is verified.

Entropic measures provide analytic tools to help us understand the stability of quantum systems. The spreading of the quantum-mechanical probability cloud for solitonic profile mass Schrödinger equation with a potential V(ax)=−V0csch2(ax) is studied in position and momentum space by means of global (Shannon’s information entropy) information-theoretic measures. The position information entropy is considered only for x>0x>0 due to the singular point at x=0x=0. The entropy densities ρs(x)ρs(x) and ρs(p)ρs(p) are demonstrated and the BBM inequality is saturated.