In this paper, we study the Cauchy problem for nonlinear Schrödinger equations with Coulomb potential $${\rm{i}}{\partial _t}u + \Delta u {K \over {\left| x \right|}}u = \lambda \right|^{p - 1}}u$$ $$1 < p \le 5\,\,{\rm{on}}\,\,{\mathbb{R}^3}$$ . Our results reveal influence of long range K∣x∣−1 on existence and scattering theories equations. particular, prove global when is attractive, i.e., K...

Evaporation is a fundamental parameter in the hydrological cycle. This study examines the performance of M5model tree and artificial neural network (ANN) models in estimating potential evapotranspiration calculated byPenman- Monteith and Hargreaves- Samani equations. Daily weather data from two meteorological stations in asemi-arid climate of Iran, namely Kerman and Zahedan, were collected duri...

We propose dynamic non-linear equations for moving surfaces in an electromagnetic field. The field is induced by a material body with a boundary of the surface. Correspondingly the potential energy, set by the field at the boundary can be written as an addition of four-potential times four-current to a contraction of the electromagnetic tensor. Proper application of the minimal action principle...

A direct rational exponential scheme is offered to construct exact multi-soliton solutions of nonlinear partial differential equation. We have considered the Calogero–Bogoyavlenskii–Schiff equation and KdV equation as two concrete examples to show efficiency of the method. As a result, one wave, two wave and three wave soliton solutions are obtained. Corresponding potential energy of the solito...

Recently F. Huang [Commun. Theor. Phys. 42 (2004) 903] and X. Tang and P.K. Shukla [Commun. Theor. Phys. 49 (2008) 229] investigated symmetry properties of the barotropic potential vorticity equation without forcing and dissipation on the beta-plane. This equation is governed by two dimensionless parameters, F and β, representing the ratio of the characteristic length scale to the Rossby radius...

In order to represent the potential energy function over the whole range of R, many potentialenergy functions have been proposed. In the present paper, we employ many potential energyfunctions, to use Numerov method for solving the nuclear Schrödinger equation for the IFmolecule, as an example of a heteronuclear diatomic molecules. Then we determine thespectroscopic constants eω , e e x ω , e B...

In this paper, new classes of symmetries for partial differential equations (PDE) which can be written in a conserved form are introduced. These new symmetries called nonclassical potential symmetries, are neither potential symmetries nor nonclassical symmetries. Some of these symmetries are carried out for the Burgers equation ut + uux − uxx = 0. (1) by studying the nonclassical symmetries of ...

Depth, number, and shape of the basins of the potential energy landscape are the key ingredients of the inherent structure thermodynamic formalism introduced by Stillinger and Weber [F. H. Stillinger and T. A. Weber, Phys. Rev. A 25, 978 (1982)]. Within this formalism, an equation of state based only on the volume dependence of these landscape properties is derived. Vibrational and configuratio...

where p, q are vector variables specifying points on L and where dq stands for the arc differential at q. As has already been pointed out (part I), this equation maynot exhibit a solution for L, but the difficulty can always be trivially obviated by a change of scale. If so, o-(q) generates potentials Oq(P), q5(P) defined by (5) and (6) of part I (Jaswon i963), where P denotes an interior or ex...