Results 31 to 40 of about 3,706 (195)
Results in Physics, 2023 This study focuses on investigating the optical soliton solutions for the perturbed nonlinear Schrödinger equation involving Kerr nonlinearity. It should be noted that the non-integrable nature of the nonlinear Schrödinger equation becomes apparent when ...
Chaoyang Zhu +3 more
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Soliton equations exhibiting Pfaffian solutions [PDF]
Glasgow Mathematical Journal, 2001 Soliton equations whose solutions are expressed by Pfaffians are briefly discussed. Included are a discrete-time Toda equation of BKP type, a modified Toda equation of BKP type, a coupled modified KdV equation and a coupled modified KdV equation of derivative type.
Hirota, Ryogo +2 more
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Complexity, 2020 In this paper, a new generalized semidiscrete integrable system with time-varying coefficients is analytically studied. Firstly, the generalized semidiscrete system is derived from a semidiscrete matrix spectral problem by embedding finite time-varying ...
Sheng Zhang, Sen Zhao, Bo Xu
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Journal of Ocean Engineering and Science, 2023 Nonlinear evolution equations (NLEEs) are frequently employed to determine the fundamental principles of natural phenomena. Nonlinear equations are studied extensively in nonlinear sciences, ocean physics, fluid dynamics, plasma physics, scientific ...
Sachin Kumar +2 more
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Duke Mathematical Journal, 1992 The authors consider the \(N\)-soliton solution to the Korteweg-de Vries equation in the limit \(N \to \infty\) by careful investigation of the spectral and scattering properties of the Schrödinger operator associated to the KdV equation by the inverse scattering transform.
Gesztesy, F., Karwowski, W., Zhao, Z.
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Advances in Difference Equations, 2020 This paper investigates the Bogoyavlenskii–Kadomtsev–Petviashvili (BKP) equation by using Hirota’s direct method and the Kadomtsev–Petviashvili (KP) hierarchy reduction method.
Wenjuan Rui, Yufeng Zhang
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Polarization Dynamics in Ferroelectrics: Insights Enabled by Machine Learning Molecular Dynamics
Advanced Science, EarlyView.Machine learning molecular dynamics is presented as a route to capture polarization switching, domain wall kinetics, topological polar textures, and polar mechanical coupling beyond the limits of conventional atomistic methods. This Perspective surveys recent progress and identifies key methodological directions, including long‐range electrostatics ...
Dongyu Bai +3 more
wiley +1 more source
Bright and Dark Soliton Solutions of the (2 + 1)-Dimensional Evolution Equations
Mathematical Modelling and Analysis, 2014 In this paper, we obtained the 1-soliton solutions of the (2+1)-dimensional Boussinesq equation and the Camassa–Holm–KP equation. By using a solitary wave ansatz in the form of sechp function, we obtain exact bright soliton solutions and another wave ...
Ahmet Bekir +3 more
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Partial Differential Equations in Applied Mathematics, 2023 Recently, mathematicians, engineers, and scientists have explored the unique characteristics and potential applications of multi-solitons, which is an expanding domain of study.
A. K. M. Kazi Sazzad Hossain +1 more
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Advancing Energy Materials by In Situ Atomic Scale Methods
Advanced Energy Materials, Volume 15, Issue 11, March 18, 2025.Progress in in situ atomic scale methods leads to an improved understanding of new and advanced energy materials, where a local understanding of complex, inhomogeneous systems or interfaces down to the atomic scale and quantum level is required. Topics from photovoltaics, dissipation losses, phase transitions, and chemical energy conversion are ...
Christian Jooss +21 more
wiley +1 more source