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We obtain novel nonlinear Schr{o}dinger-Pauli equations through a formal non-relativistic limit of appropriately constructed nonlinear Dirac equations. This procedure automatically provides a physical regularisation of potential singularities brought forward by the nonlinear terms and suggests how to regularise previous equations studied in the literature. The enhancement of contributions coming from the regularised singularities suggests that the obtained equations might be useful for future precision tests of quantum nonlinearity.
I begin by reviewing the arguments leading to a nonlinear generalisation of Schrodingers equation within the context of the maximum uncertainty principle. Some exact and perturbative properties of that equation are then summarised: those results depe
A nonlinear Schrodinger equation, that had been obtained within the context of the maximum uncertainty principle, has the form of a difference-differential equation and exhibits some interesting properties. Here we discuss that equation in the regime
We update our understanding of nonlinear Schrodinger equations motivated through information theory. In particular we show that a $q-$deformation of the basic nonlinear equation leads to a perturbative increase in the energy of a system, thus favouri
We survey the theory of attractors of nonlinear Hamiltonian partial differential equations since its appearance in 1990. These are results on global attraction to stationary states, to solitons and to stationary orbits, on adiabatic effective dynamic
By starting from the stochastic Schrodinger equation and quantum trajectory theory, we introduce memory effects by considering stochastic adapted coefficients. As an example of a natural non-Markovian extension of the theory of white noise quantum tr