Related papers: Modified Schr\"odinger equation, its analysis and …
The parametric nonlinear Schrodinger equation models a variety of parametrically forced and damped dispersive waves. For the defocusing regime, we derive a normal velocity for the evolution of curved dark-soliton fronts that represent a…
A derivation is presented of the quantummechanical wave equations based upon the Equity Principle of Einstein's General Relativity Theory. This is believed to be more generic than the common derivations based upon Einstein's energy…
The irreducible representations of the extended Galilean group are used to derive infinite sets of symmetric and asymmetric second-order differential equations with constant coeffcients. All derived equations are local and their Lagrangians…
Using the very basic physics principles, we have studied the implications of quantum corrections to classical electrodynamics and the propagation of electromagnetic waves and pulses. The initial nonlinear wave equation for the…
In this paper we start from the Schr\"odinger equation to revisit some classical quantum mechanics from the perspective of phase transition process. Here the relativistic effect of particles moving at high speed can be regarded as the phase…
For the first time, the general nonlinear Schr\"odinger equation is investigated, in which the chromatic dispersion and potential are specified by two arbitrary functions. The equation in question is a natural generalization of a wide class…
Considered is the Schr\"odinger equation in a finite-dimensional space as an equation of mathematical physics derivable from the variational principle and treatable in terms of the Lagrange-Hamilton formalism. It provides an interesting…
We consider the nonlinear Schrodinger equation with a logarithmic nonlinearity in a dispersive regime. We show that the presence of the nonlinearity affects the large time behavior of the solution: the dispersion is faster than usual by a…
Nonlinear modifications of quantum mechanics generically lead to nonlocal effects which violate relativistic causality. We study these effects using the functional Schrodinger equation for quantum fields and identify a type of nonlocality…
Is wave function collapse a prediction of the Schr\"odinger equation? This unusual problem is explored in an enlarged framework of interpretation, where quantum dynamics is considered exact and its interpretation is extended to include…
We study the existence and stability of the standing waves for the periodic cubic nonlinear Schr\"odinger equation with a point defect determined by a periodic Dirac distribution at the origin. This equation admits a smooth curve of…
The inexactness of the time-dependent Schr\"odinger equation of a charged particle in an external electromagnetic field is discussed in terms of the damping effect of the radiation. A possible improvement is to add a nonlinear term…
A nonperturbative procedure of solving the time-dependent Schr\"odinger equation, called the multi-projection approach or phase dynamics of quantum mechanics, is derived and illustrated. In addition to introducing a method with that…
The Schr\"odinger equation is universally accepted due to its excellent predictions aligning with observed results within its defined conditions. Nevertheless, it does not seem to possess the simplicity of fundamental laws, such as Newton's…
Using perturbative methods, we analyse a nonlinear generalisation of Schrodinger's equation that had previously been obtained through information-theoretic arguments. We obtain analytical expressions for the leading correction, in terms of…
We propose a new approach to the Rayleigh-Schr\"{o}dinger perturbation expansions of bound states in quantum mechanics. We are inspired by the enormous flexibility of solvable interactions with several (N) discontinuities. Their standard…
It is shown that the Schr\"{o}dinger equation for a system of interacting particles whose Compton wavelengths are of the same order of magnitude as the system size is contradictory and is not strictly nonrelativistic, because it is based on…
We consider the effect of the wind and the dissipation on the nonlinear stages of the modulational instability. By applying a suitable transformation, we map the forced/damped Nonlinear Schr\"odinger (NLS) equation into the standard NLS…
We consider an extension of the methodology of the modified method of simplest equation to the case of use of two simplest equations. The extended methodology is applied for obtaining exact solutions of model nonlinear partial differential…
It is shown that the Schr\"{o}dinger nonrelativistic equation of a system of interacting particles is not a rigorously nonrelativistic equation since it is based on the implicit assumption of finiteness of the interaction propagation…