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نتیجه جستجو - Schrödinger equation

تعداد مقالات یافته شده: 7
ردیف عنوان نوع
1 Optical solitons and other solutions to the dual-mode nonlinear Schrödinger equation with Kerr law and dual power law nonlinearities
Solitons نوری و راه حل های دیگر برای معادله Schrödinger دو حالت غیرخطی با قانون Kerr و غیرخطی های قانون قدرت دوگانه-2020
In this article, we apply four insightful integration algorithms, namely, the tanh-coth method, the unified Riccati equation method, the modified simple equation method and the new extended auxiliary equation method for constructing new optical soliton solutions and other solutions to the dual-mode nonlinear Schrödinger equation with Kerr law and dual power law nonlinearities related to the optics. Many families of Jacobi elliptic solutions, dark, bright, singular soliton solutions and other solutions have been found.
Keywords: The tanh-coth method | The unified Riccati equation method | The modified simple equation method | The new extended auxiliary equation method | Dual-mode nonlinear Schrödingers equation | Optical soliton solutions
مقاله انگلیسی
2 Invariant analysis and conservation laws of time fractional Schrödinger equations
تجزیه و تحلیل و حفاظت قوانین زمان کسری ثابت معادلات شرودینگر-2020
We study the invariance properties (symmetries) and conservation laws of the fractional time version of the nonlinear Schrödinger equation with power law nonlinearity iyt + y + y|y| = 0, α n xx for 0 < α < 1, using some recently developed approaches. We will show that the all important energy conservation due time invariance is lost due to some built in approach that the theory necessitates
Keywords: Symmetries | Conservation laws | Time fractional | Schrodinger equations
مقاله انگلیسی
3 The modified auxiliary equation method to investigate solutions of the perturbed nonlinear Schrödinger equation with Kerr law nonlinearity
روش معادله کمکی اصلاح شده برای بررسی راه حلهای معادله Schrödinger غیرخطی آشفته و غیرخطی قانون کر-2020
A variety of solitary wave solutions of the nonlinear Schrödinger equation (NLSE) with the aid of three order dispersion terms is investigated by the modified auxiliary equation method. Exact traveling wave solutions such as singular complex wave solutions and nonsingular complex wave solutions are obtained. The physical meaning of the geometrical structures for the nonsingular complex wave solutions is discussed with suitable choice of the free parameters which further characterized by bright soliton waves, stable bright periodic waves and symmetric waves.
Keywords: Exact solitary wave solutions | Schrödinger equation | The modified auxiliary equation method | Non-singular complex wave solutions
مقاله انگلیسی
4 New generalized ϕ6-model expansion method and its applications to the (3+1) dimensional resonant nonlinear Schrödinger equation with parabolic law nonlinearity
روش توسعه مدل جدید ϕ6 عمومی و برنامه های کاربردی آن در (3 + 1) معادله رزونانس بعدی غیرخطی Schrödinger با غیرخطی قانون پارابولیک-2020
In this paper, a new generalized ϕ6-model expansion method is proposed for the first time to construct optical solitons and other solutions of the (3+1) dimensional resonant nonlinear Schrödinger equation with parabolic law nonlinearity, which describes the propagation of optical pulse in nonlinear optical fibers. The generalized Jacobi elliptic function solutions and Weierstrass elliptic function solutions have been found. In particular, hyperbolic function solutions and periodic solutions are also obtained.
Keywords: New generalized ϕ6-model expansion method | New generalized Jacobi elliptic function | solutions and Weierstrass elliptic function | solutions | (3+1) dimensional resonant nonlinear | Schrödinger equation
مقاله انگلیسی
5 Long-range memory effects in a magnetized Hindmarsh-Rose neural network
اثرات حافظه با برد طولانی در یک شبکه عصبی مغناطیسی Hindmarsh-Rose-2020
We consider a model network of diffusively coupled Hindmarsh-Rose neurons to study both analytically and numerically, long-range memory effects on the modulational instabil- ity phenomenon, chaotic, synchronous and chimera states within the network. The multi- ple scale method is used to reduce the generic model into a discrete nonlinear Schrödinger equation. The latter is explored in the linear stability analysis and the instability criterion along with the critical amplitude are derived. The analytical results predict that strong lo- cal coupling, high electromagnetic induction and strong long-range interactions may sup- port the formation of highly localized excitations in neural networks. Through numeri- cal simulations, the largest Lyapunov exponents are computed for studying chaos, the synchronization factor and the strong of incoherence are recorded for studying, respec- tively synchronous and chimera states in the network. We find the appropriate domains of space parameters where these rich activities could be observed. As a result, quasi-periodic synchronous patterns, chaotic chimera and synchronous states, strange chaotic and non- chaotic attractors are found to be the main features of membrane potential coupled with memristive current during long-range memory activities of neural networks. Our results suggest that a combination of long-range activity and memory effects in neural networks may produces a rich variety of membrane potential patterns which are involved in infor- mation processing, odors recognition and discrimination and various diseases in the brain.
Keywords: Modulational instability | Chaos | Synchronization | Chimera states
مقاله انگلیسی
6 Emergent Schrödinger equation in an introspective machine learning architecture
معادله شرودینگر اضطراری در یک معماری یادگیری ماشین درون نگر-2019
Can physical concepts and laws emerge in a neural network as it learns to predict the observation data of physical systems? As a benchmark and a proof-of-principle study of this possibility, here we show an introspective learning architecture that can automatically develop the concept of the quantum wave function and discover the Schrödinger equation from simulated experimental data of the potential-todensity mappings of a quantum particle. This introspective learning architecture contains a machine translator to perform the potential to density mapping, and a knowledge distiller auto-encoder to extract the essential information and its update law from the hidden states of the translator, which turns out to be the quantum wave function and the Schrödinger equation. We envision that our introspective learning architecture can enable machine learning to discover new physics in the future.
Keywords: Quantum physics | Machine learning | Potential-to-density mapping | Neural network | Recurrent autoencoder
مقاله انگلیسی
7 Travelling and standing envelope solitons in discrete non-linear cyclic structures
مسافران و پوشش ایستادن سالیتون در ساختارهای حلقوی غیر خطی گسسته-2016
Envelope solitons are demonstrated to exist in non-linear discrete structures with cyclic symmetry. The analysis is based on the Non-Linear Schrodinger Equation for the weakly non-linear limit, and on numerical simulation of the fully non-linear equations for larger amplitudes. Envelope solitons exist for parameters in which the wave equation is focussing and they have the form of shape-conserving wave packages propagating roughly with group velocity. For the limit of maximum wave number, where the group velocity vanishes, standing wave packages result and can be linked via a bifurcation to the non-localised non-linear normal modes. Numerical applications are carried out on a simple discrete system with cyclic symmetry which can be seen as a reduced model of a bladed disk as found in turbo-machinery.& 2016 Elsevier Ltd. All rights reserved.
Keywords: Non-linear dynamics | Cyclic system | Travelling waves | Envelope soliton | Multiple scales
مقاله انگلیسی
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