3,433 research outputs found

### Group classification of (1+1)-Dimensional Schr\"odinger Equations with Potentials and Power Nonlinearities

We perform the complete group classification in the class of nonlinear
Schr\"odinger equations of the form
$i\psi_t+\psi_{xx}+|\psi|^\gamma\psi+V(t,x)\psi=0$ where $V$ is an arbitrary
complex-valued potential depending on $t$ and $x,$ $\gamma$ is a real non-zero
constant. We construct all the possible inequivalent potentials for which these
equations have non-trivial Lie symmetries using a combination of algebraic and
compatibility methods. The proposed approach can be applied to solving group
classification problems for a number of important classes of differential
equations arising in mathematical physics.Comment: 10 page

### Exact Soliton-like Solutions of the Radial Gross-Pitaevskii Equation

We construct exact ring soliton-like solutions of the cylindrically symmetric
(i.e., radial) Gross- Pitaevskii equation with a potential, using the
similarity transformation method. Depending on the choice of the allowed free
functions, the solutions can take the form of stationary dark or bright rings
whose time dependence is in the phase dynamics only, or oscillating and
bouncing solutions, related to the second Painlev\'e transcendent. In each case
the potential can be chosen to be time-independent.Comment: 8 pages, 7 figures. Version 2: stability analysis of the dark
solutio

### The relationship work of sexual intimacy in long-term heterosexual and LGBTQ partnerships

Sex is perceived as crucial to relationship success. This article reveals how sexual intimacy is part of the relationship work that couples ordinarily complete to sustain their partnerships over time. It problematizes the binary logics of good–bad sex, female–male desire, and homo–heterosexual difference and shows how fluctuations of desire and/or sexual capacity are managed by couples through intimate knowledge. Findings presented here derive from a multiple methods study with 50 long-term heterosexual and LGBTQ partnerships. I demonstrate how the absence of normative sexual scripts enables queer couples to more readily manage sexual discrepancies. Gendered differences and inequalities persist within many heterosexual relationships while reflexivity and increased openness characterizes queer coupledom. Women and LGBTQ couples are more inclined to deploy humour to diffuse difficult situations and in this context gay men are akin to women more so than heterosexual men

### Collapse of the vortex-lattice inductance and shear modulus at the melting transition in untwinned $\rm YBa_2Cu_3O_7$

The complex resistivity $\hat{\rho}(\omega)$ of the vortex lattice in an
untwinned crystal of 93-K $\rm YBa_2Cu_3O_7$ has been measured at frequencies
$\omega/2\pi$ from 100 kHz to 20 MHz in a 2-Tesla field $\bf H\parallel c$,
using a 4-probe RF transmission technique that enables continuous measurements
versus $\omega$ and temperature $T$. As $T$ is increased, the inductance ${\cal
L}_s(\omega) ={\rm Im} \hat{\rho}(\omega)/ \omega$ increases steeply to a cusp
at the melting temperature $T_m$, and then undergoes a steep collapse
consistent with vanishing of the shear modulus $c_{66}$. We discuss in detail
the separation of the vortex-lattice inductance from the `volume' inductance,
and other skin-depth effects. To analyze the spectra, we consider a weakly
disordered lattice with a low pin density. Close fits are obtained to
$\rho_1(\omega)$ over 2 decades in $\omega$. Values of the pinning parameter
$\kappa$ and shear modulus $c_{66}$ obtained show that $c_{66}$ collapses by
over 4 decades at $T_m$, whereas $\kappa$ remains finite.Comment: 11 pages, 8 figures, Phys. Rev. B, in pres

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