Results 1 to 10 of about 131,565,998 (308)
Application of the unified method to solve the ion sound and Langmuir waves model
Heliyon, 2022 We present the unified method and use it to integrate the ion sound and Langmuir waves (ISLW) model to retrieve optical soliton solutions. Some new dynamical optical solitons involving the combo of rational, trigonometric, and hyperbolic function ...
Dulal Chandra Nandi +3 more
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Towards unified AI-driven fracture mechanics: the extended deep energy method (XDEM) [PDF]
Nature CommunicationsPhysics-Informed Neural Networks (PINNs) have recently emerged as powerful tools for solving partial differential equations (PDEs), with the Deep Energy Method (DEM) proving especially effective in fracture mechanics due to its energy-based formulation ...
Yizheng Wang +10 more
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Laplace's equation on convex polyhedra via the unified method. [PDF]
Proc Math Phys Eng Sci, 2015 Ashton AC.
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Crystals, 2022 The primary purpose of this study is to analyze non-autonomous femtosecond waves with various geometrical configurations correlated to the generalized derivative nonlinear Shrödinger equation (NLSE) with variable coefficients.
Mohamed Adel +3 more
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Journal of Taibah University for Science, 2023 This paper reveals the conformable fractional space-time perturbed Gerdjikov-Ivanov (GI) equation, which is applied to nonlinear fibre optics together with photonic crystal fibres.
Qinglian Yin, Ben Gao, Zhang Shi
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A new study of soliton solutions for the variable coefficients Caudrey–Dodd–Gibbon equation
Journal of Taibah University for Science, 2022 We present a paper on the different methods for finding solutions to the Caudrey–Dodd–Gibbon equation with variable coefficients, which has wide applications in quantum mechanics and nonlinear optics.
Qinglian Yin, Ben Gao
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Unveiling parametric effects on optical solitons of the Phi-4 model in mathematical physics
Partial Differential Equations in Applied Mathematics, 2023 In the intricate realms of quantum field theory, cosmology, and condensed matter physics, the Phi-4 model emerges as a potent catalyst, shaping mathematical landscapes with profound implications. Our research has uncovered a set of soliton solutions that
Md. Abde Mannaf +5 more
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The unified technique for the nonlinear time-fractional model with the beta-derivative
Results in Physics, 2021 This present study examines the closed-form wave results (CFWRs) of the nonlinear time-fractional model (NLTFM) with Atangana’s conformable fractional derivative (ACFD) through the unified process. ACFD and its properties are included. Then, by proposing
Hijaz Ahmad +4 more
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Application of the unified method to solve the Biswas–Arshed model
Results in Physics, 2022 We apply the unified method to retrieve optical soliton solutions of the Biswas–Arshed model (BAM) with the Kerr law nonlinearity in this paper. We first derive the ordinary differential form of this model from its partial differential form via a ...
Mohammad Safi Ullah +3 more
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Initial value problem for the time-dependent linear Schrödinger equation with a point singular potential by the unified transform method [PDF]
Opuscula Mathematica, 2018 We study an initial value problem for the one-dimensional non-stationary linear Schrödinger equation with a point singular potential. In our approach, the problem is considered as a system of coupled initial-boundary value (IBV) problems on two half ...
Yan Rybalko
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