Search · four archives
Search · four archives
25 papers · ranked by Valyu relevance
S. S. Motsa, V. M. Magagula, P. Sibanda
This paper presents a new method for solving higher order nonlinear evolution partial differential equations (NPDEs). The method combines quasilinearisation, the Chebyshev spectral collocation method, and bivariate Lagrange interpolation. In this paper, we use the method to solve several nonlinear evolution equations…
Mahy Ahmed, Hamdy M. Ahmed, Niveen Badra, Islam Samir
In this study, we investigate the (2+1)-dimensional Kadomtsev-Petviashvili-Sawada-Kotera-Ramani (KPSKR) equation, a physically significant model describing nonlinear wave phenomena in higher-dimensional spaces. Utilizing the improved modified extended tanh-function method, we derive a diverse spectrum of exact…
Kamruzzaman Khan, M Ali Akbar
In this paper, we have been acquired the soliton solutions of the Variant Boussinesq equations. Primarily, we have used the enhanced (G′/G)-expansion method to find exact solutions of Variant Boussinesq equations. Then, we attain some exact solutions including soliton solutions, hyperbolic and trigonometric function…
Md Hamidul Islam, Kamruzzaman Khan, M Ali Akbar, Md Abdus Salam
Mathematical modeling of many physical systems leads to nonlinear evolution equations because most physical systems are inherently nonlinear in nature. The investigation of traveling wave solutions of nonlinear partial differential equations (NPDEs) plays a significant role in the study of nonlinear physical phenomena.…
M Ali Akbar, Norhashidah Hj Mohd Ali
The exp(-Ф(η))-expansion method is an ascending method for obtaining exact and solitary wave solutions for nonlinear evolution equations. In this article, we implement the exp(-Ф(η))-expansion method to build solitary wave solutions to the fourth order Boussinesq equation. The procedure is simple, direct and useful…
M Ali Akbar, Norhashidah Hj Mohd Ali, Syed Tauseef Mohyud-Din
Title: PACS numbers 02.30.Jr, 05.45.Yv, 02.30.Ik
Nikolay K. Vitanov, Quanmin Zhu, António Lopes
Exact solutions of nonlinear differential equations are of great importance to the theory and practice of complex systems. The main point of this review article is to discuss a specific methodology for obtaining such exact solutions. The methodology is called the SEsM, or the Simple Equations Method. The article begins…
Demei Li, Huilin Lai, Baochang Shi
In this work, we develop a mesoscopic lattice Boltzmann Bhatnagar-Gross-Krook (BGK) model to solve (2 + 1)-dimensional wave equation with the nonlinear damping and source terms. Through the Chapman-Enskog multiscale expansion, the macroscopic governing evolution equation can be obtained accurately by choosing…
Margaret Beck, Anastasia Doikou, Simon J. A. Malham, Ioannis Stylianidis
'Ioannis Stylianidis'] Abstract We develop a method for generating solutions to large classes of evolutionary partial differential systems with nonlocal nonlinearities. For arbitrary initial data, the solutions are generated from the corresponding linearized equations. The key is a Fredholm integral equation relating…
Luisiana X. Cundin
| 1 | Preface | 3 | | --- | --- | --- | | 2 | Propædeutics | 4 | | 3 | Nonlinear Convolutional Dissipative Systems | 8 | | | 3.1 Analysis | 11 | | | 3.2 Further complications | 14 | | | 3.3 An illustration | 16 | | 4 | The Classic Newell–Whitehead–Segel Equation | 18 | | | 4.1 An illustration | 23 | | 5 | Epilogue | 25…
D. T. Pham, Z. E. Musielak
Non-standard Lagrangians do not display any discernible energy-like terms, yet they give the same equations of motion as standard Lagrangians, which have easily identifiable energy-like terms. A new method to derive non-standard Lagrangians for second-order nonlinear differential equations with damping is developed and…
Christian Seifert, Sascha Trostorff, Marcus Waurick
| 1 | Introduction | | | 1 | | --- | --- | --- | --- | --- | | | 1.1 | Evolution Equations | | 1 | | | 1.2 | Time-independent Problems | . . | 3 | | | 1.3 | Evolutionary Equations | | 4 | | | 1.4 | Particular Examples and the Change of Perspective | | 5 | | | 1.5 | A Brief Outline of the Course | | 8 | | | 1.6 |…
Sascha Trostorff
Equations Authors: ['Sascha Trostorff'] | | Introduction | | 6 | | --- | --- | --- | --- | | 1. | | The framework of evolutionary problems | 12 | | | 1.1. | The Hilbert space setting and the time derivative | 12 | | | 1.2. | Evolutionary problems | 17 | | | 1.3. | Examples | 33 | | | | 1.3.1. Classical equations from…
Noureddine Mhadhbi, Sameh Gana, Mazen Fawaz Alsaeedi
This article demonstrates how variation of parameters can be successfully implemented in combination with other classical techniques, such as the method of characteristics, to derive novel classes of solutions to nonlinear partial differential equations(NLPDES) by considering specific initial conditions. This…
Stuart T. Johnston, Ruth E. Baker, Sean D.L McElwain, Matthew J. Simpson
Invasion processes are ubiquitous throughout cell biology and ecology. During invasion, individuals can become isolated from the bulk population and behave differently. We present a discrete, exclusion-based process that models the birth, death and movement of individuals. The model distinguishes between individuals…
Alex Sheremet, Yuchen Zhou, Jack P. Kennedy, Yu Qin + 2 more
Cross-frequency coupling in the hippocampus has been hypothesized to support higher-cognition functions. While gamma modulation by theta is widely accepted, evidence of phase-coupling between the two frequency components is so far unconvincing. Our observations show that theta and gamma energy increases with rat speed…
Germán Abrevaya, Aleksandr Aravkin, Guillermo Cecchi, Irina Rish + 3 more
Many real-world data sets, especially in biology, are produced by highly multivariate and nonlinear complex dynamical systems. In this paper, we focus on brain imaging data, including both calcium imaging and functional MRI data. Standard vector-autoregressive models are limited by their linearity assumptions, while…
Daniele Avitabile, Kyle Wedgwood
We study coarse pattern formation in a cellular automaton modelling a spatially-extended stochastic neural network. The model, originally proposed by Gong and Robinson [36], is known to support stationary and travelling bumps of localised activity. We pose the model on a ring and study the existence and stability of…
Sean H. Rice
Inheritance is the key factor making biological evolution possible. Despite this central role, transmission is often bundled into the simplifying assumptions of evolutionary models, making it difficult to see how changes in the patterns of transmission influence evolutionary dynamics. We present a mathematical…
Nikolay K. Vitanov, Zlatinka I. Dimitrova
We discuss a version the methodology for obtaining exact solutions of nonlinear partial differential equations based on the possibility for use of: (i) more than one simplest equation; (ii) relationship that contains as particular cases the relationship used by Hirota [1] and the relationship used in the previous…
Authors not listed
Two-dimensional electronic spectroscopy (2DES) is a powerful experimental technique, as it directly probes the nonlinear (third-order) response function of the system, providing key insights into ultrafast energy transfer and relaxation processes. However, 2DES experiments are generally difficult to interpret, often…
Francesco Talotta, David Lauvergnat, Federica Agostini
The exact factorization of the electron-nuclear wavefunction is applied to the study of the photo- isomerization of a retinal chromophore model. We describe such an ultrafast nonadiabatic process by analyzing the time-dependent potentials of the theory and by mimicking nuclear dynamics with quantum and coupled…
Authors not listed
Strong coupling and environmental memory render many open quantum systems intractable to classical computation. To overcome this barrier, we present a variational quantum algorithm capable of solving generalized form time-local quantum master equations directly on Noisy Intermediate-Scale Quantum (NISQ) processors. Our…
Authors not listed
The GENERIC framework provides a robust structure for nonequilibrium dynamics but lacks a principled method to select reversible ($L$) and irreversible ($M$) brackets. Similarly, finite-time optimizations minimizing path-averaged reciprocal temperature exist but remain isolated. Here, we introduce the \textbf{Entropy…
Authors not listed
Inverse problems, where we seek the values of inputs to a model that lead to a desired set of outputs, are a challenges subset of problems in science and engineering. In this work we demonstrate the use of two generative AI methods to solve inverse problems. We compare this approach to two more conventional approaches…