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 …
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 …
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) …
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 …
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
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 …
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 …
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
We perform a detailed study on the completely non-integrable forced damped
Gardner/Extended Kawahara equation (FDEKE). Three techniques are introduced to …
Gardner/Extended Kawahara equation (FDEKE). Three techniques are introduced to …
Novel analytical approximations to the nonplanar Kawahara equation and its plasma applications
In this paper, some novel analytical approximations to a completely non-integrable
nonplanar (cylindrical and spherical) Kawahara equation (nKE) are derived. Using the …
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) …
describe the propagations of nonlinear waves. In this paper, we investigate the (2+ 1) …
Extended shallow water wave equations
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 …
expansions, from the Euler (or water wave) equations. These extended models are valid one …