Results 51 to 60 of about 36,271 (185)

On a fourth order nonlinear Helmholtz equation [PDF]

, 2018
In this paper, we study the mixed dispersion fourth order nonlinear Helmholtz equation $\Delta^2 u -\beta \Delta u + \alpha u= \Gamma|u|^{p-2} u$ in $\mathbb R^N$ for positive, bounded and $\mathbb Z^N$-periodic functions $\Gamma$.
Abramowitz M., Bonheure D., Bonheure D., Denis Bonheure, Evéquoz G., Gilbarg D., Jean‐Baptiste Casteras, Lorenzi L., Rainer Mandel, Stein E. M., Stein E. M., Sulem C.   +11 more
core   +3 more sources

AI‐Guided Co‐Optimization of Advanced Field‐Effect Transistors: Bridging Material, Device, and Fabrication Design

Advanced Intelligent Discovery, EarlyView.
This article outlines how artificial intelligence could reshape the design of next‐generation transistors as traditional scaling reaches its limits. It discusses emerging roles of machine learning across materials selection, device modeling, and fabrication processes, and highlights hierarchical reinforcement learning as a promising framework for ...
Shoubhanik Nath, Shauryaraj K. Jilkar, Aditya Udgaonkar, Yu (Joe) Lu, Ali Mesbah   +4 more
wiley   +1 more source

A Hybrid Semi‐Inverse Variational and Machine Learning Approach for the Schrödinger Equation

Advanced Physics Research, EarlyView.
A hybrid semi‐inverse variational and machine‐learning framework is presented for solving the Schrödinger equation with complex quantum potentials. Physics‐based variational solutions generate high‐quality training data, enabling Random Forest and Neural Network models to deliver near‐perfect energy predictions.
Khalid Reggab, Houssam Eddine Hailouf, Kingsley Onyebuchi Obodo, Mireille Megnidio‐Tchoukouegno, Mohammed Benali Kanoun, Souraya Goumri‐Said   +5 more
wiley   +1 more source

Riemann–Hilbert approach and N-soliton solution for an eighth-order nonlinear Schrödinger equation in an optical fiber

Advances in Difference Equations, 2019
This paper aims to present an application of the Riemann–Hilbert approach to treat higher-order nonlinear differential equation that is an eighth-order nonlinear Schrödinger equation arising in an optical fiber. Starting from the spectral analysis of the
Zhou-Zheng Kang, Tie-Cheng Xia, Wen-Xiu Ma   +2 more
doaj   +1 more source

Jacobi elliptic function approach to a conformable fractional nonlinear Schrödinger–Hirota equation

Partial Differential Equations in Applied Mathematics, 2023
In this present paper we propound the following equation iDtαu+a2Dx2αu+ia3Dx3αu+a4Dx4α+ibDxα|u|2u+iσ|u|2Dxαu+iλDxα|u|2=c1|u|2u+c2|u|4,which is called the generalized nonlinear fractional Schrödinger–Hirota equation with conformable derivative.
Ahmad Sharif
doaj   +1 more source

Self‐Similar Blowup for the Cubic Schrödinger Equation

Communications on Pure and Applied Mathematics, EarlyView.
ABSTRACT We give a rigorous proof for the existence of a finite‐energy, self‐similar solution to the focusing cubic Schrödinger equation in three spatial dimensions. The proof is computer‐assisted and relies on a fixed point argument that shows the existence of a solution in the vicinity of a numerically constructed approximation.
Roland Donninger, Birgit Schörkhuber
wiley   +1 more source

Complex optical solutions and modulation instability of hyperbolic Schrödinger dynamical equation

Results in Physics, 2019
Complex hyperbolic Schrödinger equation describes ultra-short pulse propagation in nonlinear media fiber optics. In this paper, new complex solutions for the complex hyperbolic Schrödinger equation are constructed using generalized elliptic equation ...
Wilson Osafo Apeanti, Aly R. Seadawy, Dianchen Lu   +2 more
doaj   +1 more source

Solitary wave solutions of the Camassa–Holm-Nonlinear Schrödinger Equation

Results in Physics, 2020
This study investigates the solitary wave solutions to the defocusing nonlinear Schrödinger equation, which is known as Camassa–Holm-Nonlinear Schrödinger (CH-NLS) equation.
Thilagarajah Mathanaranjan
doaj   +1 more source

Semiclassical stationary states for nonlinear Schr\"odinger equations under a strong external magnetic field [PDF]

, 2015
We construct solutions to the nonlinear magnetic Schr\"odinger equation $$ \left\{ \begin{aligned} - \varepsilon^2 \Delta_{A/\varepsilon^2} u + V u &= \lvert u\rvert^{p-2} u & &\text{in}\ \Omega,\\ u &= 0 & &\text{on}\ \partial\Omega, \end{aligned}
Di Cosmo, Jonathan, Van Schaftingen, Jean   +1 more
core   +2 more sources

Generalized Chemical Model for Warm Dense Hydrogen: Ionization Potential Depression and Molecular Dissociation Shifts

Contributions to Plasma Physics, EarlyView.
ABSTRACT Warm dense matter (WDM) is a complex state, where quantum effects, thermal excitations, and strong interparticle correlations coexist. Understanding its microscopic composition and medium‐induced modifications of atomic and molecular properties is essential for planetary modeling, fusion research, and high‐energy‐density experiments.
L. T. Yerimbetova, Yu. V. Arkhipov, Ye. S. Mukhametkarimov, A. E. Davletov, I. M. Tkachenko   +4 more
wiley   +1 more source