We study solitary wave solutions of the higher order nonlinear Schrodinger equation for propagation short light pulses in an optical fiber. Using a scaling transformation we reduce to two-parameter canonical form. Solitary (1-soliton) exist provided easily met inequality constraints on parameters are satisfied. Conditions existence N-soliton (N>1) determined; when these conditions becomes modified KdV equation. A proper subset meet Painleve plausibility integrability.

Tenured Bosses and Disposable Teachers: Writing Instruction in the Managed University exposes poor working conditions of contingent composition faculty explores practical alternatives to unfair labor practices that are all too common on campuses today. Editors Marc Bousquet, Tony Scott, Leo Parascondola bring together diverse perspectives from pragmatism historical materialism provide a perceptive engaging examination nature, extent, economics managed problem instructiona field which as much...

We re-examine the mathematical properties of kink and antikink soliton solutions to Logarithmic Schrödinger Equation (LogSE), a nonlinear logarithmic version incorporating Everett–Hirschman entropy. devise successive approximations with increasing accuracy. From most successful forms, we formulate an analytical solution that provides very accurate LogSE. Finally, consider combinations such mathematically model bound states, which can serve as possible candidate for modeling dilatonic quantum...

Herein, we present a sequel to earlier work on generalization of the Lambert W function. In particular, examine series expansions generalized version providing computational means for evaluating this function in various regimes and further confirming notion that is natural nextension standard

In order to clarify questions about the calculation of exchange energy a homonuclear molecular ion, an analysis is carried out model problem consisting one-dimensional limit H2+. It demonstrated that use infinite polarization expansion for localized wave function in Holstein–Herring formula yields approximate which at large internuclear distances R has correct leading behavior O(e−R) and close but not equal exact energy. The extension n-dimensional double-well presented.

Using a rapidly convergent composite basis of Frankowski-Pekeris and Frankowski functions, we have accurately calculated the nodal surfaces low-lying excited states helium atom to investigate Bressanini Reynolds' conjecture [D. P. J. Reynolds, Phys. Rev. Lett. 95, 110201 (2005)] that these are rigorously independent interelectronic angle ${\ensuremath{\theta}}_{12}$. We find in fact there is slight dependence on ${\ensuremath{\theta}}_{12}$, but it so small assumption strict independence may...

Herein, we use Hardy's notion of the "false derivative" to obtain exact multiple roots in closed form transcendental-algebraic equations representing generalized Lambert W function. In this fashion, flesh out function by complementing previous developments produce a more complete and integrated body work. Finally, demonstrate usefulness special with some applications.

We generalize the 1+1-dimensional gravity formalism of Ohta and Mann to 3+1 dimensions by developing canonical reduction a proposed applied system coupled with set point particles. This is done via Arnowitt-Deser-Misner method eliminating resulting constraints imposing coordinate conditions. The reduced Hamiltonian completely determined in terms particles' variables (coordinates, dilaton field momenta). It found that equation governing under suitable gauge conditions, including absence...

This article draws on qualitative research conducted as a part of writing program assessment to examine the relationship between assessment, valuation, and economics first-year writing. It argues that terms labor in complicate practices valuation processes consensus building have become common models. explains if is be situated at site represent work happens there faithfully, it needs account for how power, staffing, differing ways thinking about education necessitate struggle acknowledgment...

We study the (pseudo-) anyon Hubbard model on a one-dimensional lattice without presence of three-body hardcore constraint. In particular, for pseudo-fermion limit large statistical angle $\ensuremath{\theta}\ensuremath{\approx}\ensuremath{\pi}$, we observe wealth exotic properties, including first-order transition between different superfluid phases and two-component partially paired phase fillings need an additional this limit, analyze effect induced constraint, which leads to...

Experimental data suggests that, at temperatures below 1 K, the pressure in liquid helium has a cubic dependence on density. Thus speed of sound scales as root pressure. Near critical point, this approaches zero whereby is negative, thus indicating cavitation instability regime. We demonstrate that to explain dependence, one view mixture three quantum Bose liquids: dilute (Gross–Pitaevskii-type) Bose–Einstein condensate, Ginzburg–Sobyanin-type fluid, and logarithmic superfluid. Therefore,...

This article presents research from a qualitative study of the way that reflective writing is solicited, taught, composed, and assessed within state-mandated portfolio curriculum. The situates texts generated by participating students larger goals bureaucratic processes school system. finds letters are genre state curriculum regulates substance tone students’ reflections. At classroom level, provides mode adopt with assurance their reflections will meet evaluators’ expectations. helps to...

Herein, we present a canonical form for natural and necessary generalization of the Lambert W function, in that it requires minimal mathematical definitions this generalization, provides means expressing solutions to number physical problems fundamental nature. In particular, expresses exact general-relativistic self-gravitating 2-body 3-body systems one spatial time dimension. It also solution previously unknown link between lineal gravity problem Schroedinger equation.

Tang, Toennies, and Yiu have shown that unsymmetrized Rayleigh-Schr\"odinger perturbation theory can be used to calculate the leading terms in ground-state exchange energy of ${\mathrm{H}}_{2}^{+}$ using method Holstein Herring. We clarify this seemingly puzzling result by showing their approximation polarization wave function is exactly he term Herring-Holstein function. also show a generalization yields asymptotic for excited states, thereby suggesting existence general underlying property...

The fixed-node variant of the diffusion quantum Monte Carlo method (FN-DMC) is capable obtaining exact eigenvalues (albeit numerically with statistical error) a many-electron Hamilton operator, provided that nodal hypersurface wave function given. use nodes trial leads to node location error. authors have developed local criteria assess accuracy based on distances hypersurfaces PsiT, TPsiT, and HPsiT which coincide for function. These are used develop direct optimization methods...