Pfaffian, breather, and hybrid solutions for a (2+ 1)-dimensional generalized nonlinear system in fluid mechanics and plasma physics

CD Cheng, B Tian, YX Ma, TY Zhou, Y Shen - Physics of Fluids, 2022 - pubs.aip.org
Fluid mechanics is seen as the study on the underlying mechanisms of liquids, gases and
plasmas, and the forces on them. In this paper, we investigate a (2+ 1)-dimensional …

State-of-the-art review of design of experiments for physics-informed deep learning

S Das, S Tesfamariam - arXiv preprint arXiv:2202.06416, 2022 - arxiv.org
This paper presents a comprehensive review of the design of experiments used in the
surrogate models. In particular, this study demonstrates the necessity of the design of …

Pfaffian solutions and nonlinear waves of a (3+ 1)-dimensional generalized Konopelchenko–Dubrovsky–Kaup–Kupershmidt system in fluid mechanics

Y Shen, B Tian, CD Cheng, TY Zhou - Physics of Fluids, 2023 - pubs.aip.org
Fluid mechanics is concerned with the behavior of liquids and gases at rest or in motion,
where the nonlinear waves and their interactions are important. Hereby, we study a (3+ 1) …

Shallow-water-wave studies on a (2+ 1)-dimensional Hirota–Satsuma–Ito system: X-type soliton, resonant Y-type soliton and hybrid solutions

Y Shen, B Tian, TY Zhou, XT Gao - Chaos, Solitons & Fractals, 2022 - Elsevier
Water waves can be seen in the rivers, lakes, oceans, etc. A (2+ 1)-dimensional Hirota–
Satsuma–Ito system, which arises in the shallow water waves, is investigated in this work …

On the analytical approximations to the nonplanar damped Kawahara equation: Cnoidal and solitary waves and their energy

SA El-Tantawy, LS El-Sherif, AM Bakry, W Alhejaili… - Physics of …, 2022 - pubs.aip.org
In this work, the non-integrable nonplanar (cylindrical and spherical) damped Kawahara
equation (ndKE) is solved and analyzed analytically. The ansatz method is implemented for …

Solving partial differential equations using deep learning and physical constraints

Y Guo, X Cao, B Liu, M Gao - Applied Sciences, 2020 - mdpi.com
The various studies of partial differential equations (PDEs) are hot topics of mathematical
research. Among them, solving PDEs is a very important and difficult task. Since many …

On the analytical and numerical approximations to the forced damped Gardner Kawahara equation and modeling the nonlinear structures in a collisional plasma

HA Alyousef, AH Salas, RT Matoog, SA El-Tantawy - Physics of Fluids, 2022 - pubs.aip.org
We perform a detailed study on the completely non-integrable forced damped
Gardner/Extended Kawahara equation (FDEKE). Three techniques are introduced to …

Novel analytical approximations to the nonplanar Kawahara equation and its plasma applications

MR Alharthi, RA Alharbey, SA El-Tantawy - The European Physical …, 2022 - Springer
In this paper, some novel analytical approximations to a completely non-integrable
nonplanar (cylindrical and spherical) Kawahara equation (nKE) are derived. Using the …

Hybrid solutions for the (2+ 1)-dimensional variable-coefficient Caudrey-Dodd-Gibbon-Kotera-Sawada equation in fluid mechanics

FY Liu, YT Gao, X Yu, L Hu, XH Wu - Chaos, Solitons & Fractals, 2021 - Elsevier
In fluid mechanics, the higher-dimensional and higher-order equations are constructed to
describe the propagations of nonlinear waves. In this paper, we investigate the (2+ 1) …

Extended shallow water wave equations

TP Horikis, DJ Frantzeskakis, NF Smyth - Wave Motion, 2022 - Elsevier
Extended shallow water wave equations are derived, using the method of asymptotic
expansions, from the Euler (or water wave) equations. These extended models are valid one …