3,433 research outputs found

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

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    We perform the complete group classification in the class of nonlinear Schr\"odinger equations of the form iψt+ψxx+ψγψ+V(t,x)ψ=0i\psi_t+\psi_{xx}+|\psi|^\gamma\psi+V(t,x)\psi=0 where VV is an arbitrary complex-valued potential depending on tt and x,x, γ\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

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    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

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    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 YBa2Cu3O7\rm YBa_2Cu_3O_7

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    The complex resistivity ρ^(ω)\hat{\rho}(\omega) of the vortex lattice in an untwinned crystal of 93-K YBa2Cu3O7\rm YBa_2Cu_3O_7 has been measured at frequencies ω/2π\omega/2\pi from 100 kHz to 20 MHz in a 2-Tesla field Hc\bf H\parallel c, using a 4-probe RF transmission technique that enables continuous measurements versus ω\omega and temperature TT. As TT is increased, the inductance Ls(ω)=Imρ^(ω)/ω{\cal L}_s(\omega) ={\rm Im} \hat{\rho}(\omega)/ \omega increases steeply to a cusp at the melting temperature TmT_m, and then undergoes a steep collapse consistent with vanishing of the shear modulus c66c_{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 ρ1(ω)\rho_1(\omega) over 2 decades in ω\omega. Values of the pinning parameter κ\kappa and shear modulus c66c_{66} obtained show that c66c_{66} collapses by over 4 decades at TmT_m, whereas κ\kappa remains finite.Comment: 11 pages, 8 figures, Phys. Rev. B, in pres