Exact solutions to the Dirac-Born-Infeld equation, which describes scat-terings of localized wave packets in the presence of constant background fields, are derived in this paper.

The neutrino oscillation phenomenon has been discussed in the case of neutrinos propagating in a flat space–time both in the plane wave approach for highly relativistic neutrinos [1] and in the wave packet formalism [2]. In this note we present a generalization of the plane wave approach to the case of curved space–time [3–5]. In order to generalize the plane–wave approach to the case of a curv...

This article concerns the dressing method for solving of multidimensional nonlinear Partial Differential Equations. In particular, we join hierarchy of matrix Burgers type equation with hierarchies of equations integrable by the Inverse Spectral Transform (IST). Example of resonance interaction of wave packets in (3+1)-dimensions is given.

I refute the criticisms of Ref. [1] raised in Ref. [2]. With this short note I would like to answer the rather provocative note of Okun, Rotaev, Schepkin and Tsukerman (O.R.S.T.) in Ref. [2]. First, I would like to thank O.R.S.T. for their attention to my recent paper in Ref. [1], that is the object of their criticism. The specific target of the O.R.S.T. criticism is the use of the substitution...

Although real, normalized Gaussian wave packets minimize the product of position and momentum uncertainties, generic complex normalized Gaussian wave packets do not. We prove they minimize an alternative product of uncertainties that correspond to variables that are phase space rotations of position and momentum.

Stimulated by a remark of J. L. Doob at the beginning of Appendix I to Kai Lai Chung’s English translation “Limit Distributions for Sums of Independent Variables” of the Russian classic by B. V. Gnedenko and A. N. Kolmogorov [5] we highlight the somewhat nonprobabilistic importance of characteristic functions and their positive definiteness property in a pedagogical attempt to introduce the not...