Search · four archives
Search · four archives
25 papers · ranked by Valyu relevance
A. S. Fokas
There are integrable nonlinear evolution equations in two spatial variables. The solution of the initial value problem of these equations necessitated the introduction of novel mathematical formalisms. Indeed, the classical Riemann-Hilbert problem used for the solution of integrable equations in one spatial variable…
Elsayed M.E. Zayed, Mona El–Shater, Ahmed H. Arnous, Anjan Biswas
In numerous fields of mathematical physics, including nuclear physics, fluid dynamics, quantum optics, and plasma physics, the idea of nonlinear evolution equation has left an enduring impression. The concept of concatenation model has recently gained its popularity after its first appearance during 2014. Such a model…
Wafy M. Hasan, Hamdy M. Ahmed, Ahmed M. Ahmed, Haytham M. Rezk + 1 more
A fifth-order nonlinear partial differential equation is analyzed to construct exact traveling wave solutions through the modified extended mapping method. By converting the governing equation into an equivalent ordinary differential form, the approach enables the derivation of multiple classes of analytical solutions…
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…
A. Hussain, T. Parveen, B. A. Younis, Huda U. M. Ahamd + 2 more
'T. F. Ibrahim' 'Mohammed Sallah'] Utilizing nonlinear evolution equations (NEEs) is common practice to establish the fundamental assumptions underlying natural phenomena. This paper examines the weakly dispersed non-linear waves in mathematical physics represented by the Konopelchenko-Dubrovsky (KD) equations. The…
Shariful Islam, Bishnupada Halder, Ahmed Refaie Ali
In this study, the uses of unified method for finding solutions of a nonlinear Schrödinger equation that describes the nonlinear spin dynamics of (2+1) dimensional Heisenberg ferromagnetic spin chains equation. We successfully construct solutions to these equations. For each of the derived solutions, we provide the…
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…
Umar Muhammad Dauda, Lawal Ja'afaru
This study employs spectral methods to capture the behaviour of wave equation with dispersive-nonlinearity. We describe the evolution of hump initial data and track the conservation of the mass and energy functionals. The dispersive-nonlinearity results to solution in an extended Schwartz space via analytic approach.…
Nikolay K. Vitanov
Transformations are much used to connect complicated nonlinear differential equations to simple equations with known exact solutions. Two examples of this are the Hopf–Cole transformation and the simple equations method. In this article, we follow an idea that is opposite to the idea of Hopf and Cole: we use…
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…
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…
Hina Zulfiqar, Shenglan Yuan, Muhammad Shoaib Saleem
under the effect of L\'evy noise Authors: ['Hina Zulfiqar' 'Shenglan Yuan' 'Muhammad Shoaib Saleem'] This study aims to examine the effect of L´evy noise on the solutions of the nonlinear Schr ¨odinger equation. An improved diversity of stochastic solutions is instinctively located discretely on certain conditions by…
Megan Morrison, J. Nathan Kutz
Nonlinear ordinary differential equations can rarely be solved analytically. Koopman operator theory provides a way to solve nonlinear systems by mapping nonlinear dynamics to a linear space using eigenfunctions. Unfortunately, finding such eigenfunctions is difficult. We introduce a method for constructing…
Nilormy Gupta Trisha, Md. Shafiqul Islam
The purpose of this research work is to employ the Optimal Auxiliary Function Method (OAFM) for obtaining numerical approximations of time-dependent nonlinear partial dierential equations (PDEs) that arise in many disciplines of science and engineering. The initial and rst approximations of parabolic nonlinear PDEs…
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…
Abiam Tamburrini, Sergio Davis, Diego González, Pablo S. Moya + 1 more
In this work, we formulate a systematic expectation-value framework for dynamical systems whose probability densities evolve according to linear partial differential equations, such as the Fokker-Planck and Liouville equations. The approach is based on expectation-calculus identities associated with the…
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…
Mauricio González-Forero
Mathematically integrating genetics, development, and evolution is a longstanding challenge. Here I develop general mathematical theory that integrates sexual, discrete, multilocus genetics, development, and evolution. This yields an exact method to describe the evolutionary dynamics of allele frequencies and linkage…
D.T. Pham, Z.E. Musielak
The Lagrangian formalism is developed for the population dynamics of interacting species that are described by several well-known models. The formalism is based on standard Lagrangians, which represent differences between the physical kinetic and potential energy-like terms. A method to derive these Lagrangians is…
Ismaila Muhammed, Dimitris M. Manias, Dimitris A. Goussis, Haralampos Hatzikirou
Biomedical systems inherently exhibit multi-scale dynamics, making accurate system identification particularly challenging due to the complexity of capturing a wide time scale spectrum. Traditional methods capable of addressing this issue rely on explicit equations, limiting their applicability in cases where only…
Soha Ben Tahar, Jose J Muñoz, Sandra J Shefelbine, Ester Comellas
Reaction-diffusion systems have been widely used to model pattern formation in biological systems. However, the emergence of Turing patterns in three-dimensional (3D) domains remains relatively unexplored. A few studies on this topic have shown that extending pattern formation from 2D to 3D is not straightforward.…
George Bayliss, Jared C. Bronski
The Evans function is an analytic function that encodes information about the intersection of certain subspaces in ODE boundary value problems. As such it is a useful tool for computing the spectrum of boundary value problems arising in the stability of coherent structures. In typical applications one is interested in…
Loïc Marrec, Claudia Bank, Thibault Bertrand
Population growth is a fundamental process in ecology, evolution, and epidemiology. The population size dynamics during growth are often described by deterministic equations derived from kinetic models. Here, we simulate several population growth models and compare the size averaged over many stochastic realizations…
Authors not listed
Molecular dynamics (MD) and hybrid quantum–classical (QM/MM) methods provide powerful tools for simulating chemical and biological systems, yet their application to long-timescale, strongly coupled processes remains limited by non-integrability, chaotic sensitivity, and extreme time-scale separation. These limitations…
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…