Results 41 to 50 of about 3,339,817 (343)
Hypergeometric solutions to Schrödinger equations for the quantum Painlevé equations [PDF]
, 2011 We consider Schr\"odinger equations for the quantum Painlev\'e equations. We present hypergeometric solutions of the Schr\"odinger equations for the quantum Painlev\'e equations, as particular solutions. We also give a representation theoretic correspondence between Hamiltonians of the Schr\"odinger equations for the quantum Painlev\'e equations and ...
arxiv +1 more source
A study on the bilinear equation of the sixth Painlevé transcendents [PDF]
arXiv, 2023 The sixth Painlev\'e equation is a basic equation among the non-linear differential equations with three fixed singularities, corresponding to Gauss's hypergeometric differential equation among the linear differential equations. It is known that 2nd order Fuchsian differential equations with three singular points are reduced to the hypergeometric ...
arxiv
Journal of Physics: Theories and Applications, 2020 The application bispherical coordinates in Schrödinger equation for the Mobius square plus modified Yukawa potential have been obtained. The Schrödinger equation in bispherical coordinates for the separable Mobius square plus modified Yukawa potential ...
Briant Sabathino Harya Wibawa +2 more
doaj +1 more source
Deep learning and the Schrödinger equation [PDF]
arXiv.org, 2017 A deep (convolutional) neural network is trained to predict the ground-state energy of an electron in two-dimensional potentials. The machinery of deep learning is developed to learn the mapping between potential and energy, which bypasses the need to ...
Kyle Mills, M. Spanner, Isaac Tamblyn
semanticscholar +1 more source
Inverse scattering transform for the nonlocal nonlinear Schrödinger equation with nonzero boundary conditions [PDF]
, 2016 In 2013, a new nonlocal symmetry reduction of the well-known AKNS (an integrable system of partial differential equations, introduced by and named after Mark J. Ablowitz, David J. Kaup, and Alan C. Newell et al. (1974)) scattering problem was found.
M. Ablowitz, Xu‐Dan Luo, Z. Musslimani
semanticscholar +1 more source
Exact Multisoliton Solutions of General Nonlinear Schrödinger Equation with Derivative
The Scientific World Journal, 2014 Multisoliton solutions are derived for a general nonlinear Schrödinger equation with derivative by using Hirota’s approach. The dynamics of one-soliton solution and two-soliton interactions are also illustrated.
Qi Li, Qiu-yuan Duan, Jian-bing Zhang
doaj +1 more source
The mixed coupled nonlinear Schrödinger equation on the half-line via the Fokas method
Proceedings of the Royal Society A, 2016 In this paper, we implement the Fokas method to study initial-boundary value problems of the mixed coupled nonlinear Schrödinger equation formulated on the half-line with Lax pairs involving 3×3 matrices.
Shou‐Fu Tian
semanticscholar +1 more source
A Spacetime DPG Method for the Schrödinger Equation [PDF]
SIAM Journal on Numerical Analysis, 2016 A spacetime discontinuous Petrov--Galerkin (DPG) method for the linear time-dependent Schrodinger equation is proposed. The spacetime approach is particularly attractive for capturing irregular solutions.
L. Demkowicz +3 more
semanticscholar +1 more source
Alkane biosynthesis gene expression and its increased production in recombinant cyanobacteria
FEBS Open Bio, EarlyView.The transcription and mRNA structures of the alkane biosynthesis genes ado/aar were analysed in the representative cyanobacteria PCC 6803 and SK1‐2‐1, which produce C17H36 and C15H32, respectively. PCC 6803 transconjugants carrying these genes showed a 1.8‐ to 2.3‐fold increase in C17H36 production.
Misato Nagao +4 more
wiley +1 more source
On the Definition of Chirality and Enantioselective Fields
Israel Journal of Chemistry, Volume 62, Issue 11-12, December 2022., 2022 Abstract In solid state physics, any symmetry breaking is known to be associated with emergence of an order parameter. However, the order parameter for molecular and crystal chirality, which is a consequence of parity and mirror symmetry breaking, has not been known since its discovery.
Jun‐ichiro Kishine +2 more
wiley +1 more source