23 papers · ranked by Valyu relevance
Nikolay K. Vitanov, Zlatinka I. Dimitrova, Kaloyan N. Vitanov
The goal of this article is to discuss the Simple Equations Method (SEsM) for obtaining exact solutions of nonlinear partial differential equations and to show that several well-known methods for obtaining exact solutions of such equations are connected to SEsM. In more detail, we show that the Hirota method is…
Bilige Sudao, Xiaomin Wang, Vanesa Magar
In this paper, a generalized simplest equation method is proposed to seek exact solutions of nonlinear evolution equations (NLEEs). In the method, we chose a solution expression with a variable coefficient and a variable coefficient ordinary differential auxiliary equation. This method can yield a Bäcklund…
Nikolay K. Vitanov, Zlatinka I. Dimitrova
We discuss a new version of a method for obtaining exact solutions of nonlinear partial differential equations. We call this method the Simple Equations Method (SEsM). The method is based on representation of the searched solution as function of solutions of one or several simple equations. We show that SEsM contains…
Nikolay K. Vitanov, Zlatinka I. Dimitrova, Hölger Kantz
The modified method of simplest equation is applied to the extended Korteweg - de Vries equation and to generalized Camassa - Holm equation. Exact traveling wave solutions of these two nonlinear partial differential equations are obtained. The equations of Bernoulli, Riccati and the extended tanh - equation are used as…
Nikolay K. Vitanov
We discuss an extension of the modified method of simplest equation for obtaining exact analytical solutions of nonlinear partial differential equations. The extension includes the possibility for use of: (i) more than one simplest equation; (ii) relationship that contains as particular cases the relationship used by…
Nikolay K. Vitanov, Zlatinka I. Dimitrova, Kaloyan N. Vitanov
We discuss the application of a variant of the method of simplest equation for obtaining exact traveling wave solutions of a class of nonlinear partial differential equations containing polynomial nonlinearities. As simplest equation we use differential equation for a special function that contains as particular cases…
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…
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…
Ivan P. Jordanov, Nikolay K. Vitanov
We discuss a class of hyperbolic reaction-diffusion equations and apply the modified method of simplest equation in order to obtain an exact solution of an equation of this class (namely the equation that contains polynomial nonlinearity of fourth order). We use the equation of Bernoulli as a simplest equation and…
Elena V. Nikolova, António Lopes
We apply the Simple Equations Method (SEsM) for obtaining exact travelling-wave solutions of the extended fifth-order Korteweg-de Vries (KdV) equation. We present the solution of this equation as a composite function of two functions of two independent variables. The two composing functions are constructed as finite…
Zlatinka I. Dimitrova
Many complex systems are nonlinear [?]- [14]. Usually, the effects connected to nonlinearity are studied by the methods of the time series analysis or are modeled by nonlinear differential or difference equations [15] - [31]. The methodology for obtaining exact solutions of nonlinear differential equation was in…
Authors not listed
While the method of manual inspection reliably produces correct results at the introductory level, it can often appear untidy and unintuitive and lacks teachable depth. This paper presents a novel alternative approach designed to achieve the same outcomes as manual inspection but with enhanced clarity. It serves as…
Inga Timofejeva, Tadas Telksnys, Zenonas Navickas, Romas Marcinkevicius + 1 more
'Romas Marcinkevicius' 'Minvydas Ragulskis'] A meta-model of diffusively coupled Lotka-Volterra systems used to model various biomedical phenomena is considered in this paper. Necessary and sufficient conditions for the existence of nth order solitary solutions are derived via a modified inverse balancing technique. It…
Authors not listed
A method has been introduced to derive the solution of the time-independent Schrodinger equation for the simple harmonic oscillator. A trial solution has been chosen as the product of the divergent part of the approximate asymptomatic solution of the Schrodinger equation and an unknown function. By inserting this trial…
Caroline Cannistra, Kyle Medley, Herbert M. Sauro
In this technical report we describe a simple extension to python-libSBML that allows users of Python to more easily construct SBML based models. The most commonly used package for constructing SBML models in Python is python-libSBML based on the C/C++ library libSBML. python-libSBML supports a comprehensive set of…
Authors not listed
This document presents a comprehensive heuristic algorithm for the teaching and practice of fundamental inorganic chemistry in representative elements. A logical-deductive method is proposed, starting from the electronic configuration and Hund’s Maximum Multiplicity Principle to determine valence by counting unpaired…
Anton V. Sinitskiy
This study presents a novel, highly simplified model of the nervous system, inspired by one hypothetical scenario of its origin. The model is designed to accommodate both mathematical derivations and numerical simulations, offering a template for studying generalized principles and dynamics beyond the specifics of the…
Wylie Stroberg, Santiago Schnell
The simple bimolecular ligand–receptor binding interaction is often linearized by assuming pseudo-first-order kinetics when one species is present in excess. Here, a phase-plane analysis allows the derivation of a new condition for the validity of pseudo-first-order kinetics that is independent of the initial receptor…
Authors not listed
This paper introduces Post-Inspection Analysis (PIA), a concept for understanding and reverse engineering balanced equations of similar reactions. Here we explore the idea that balanced equations contain useable information observed by grouping and analysing similar equations, allowing us to uncover observations that…
Anton V. Sinitskiy
This paper extends our previous work on the simplest model of a nervous system by providing an asymptotic analysis of the evolutionarily optimal solution in this model. Building on the formalism and principles established earlier, we derive an asymptotic solution to the Fokker-Planck-Kolmogorov equation for a given…
Anton V. Sinitskiy
In this paper, we extend our previous work on a simplified model of the nervous system by solving the general optimization problem for the evolutionary cost of the nervous system. This optimization takes into account constraints on the scales of membrane potential kinetics and sensory response function to ensure…
O. Ebenhöh, M. van Aalst, N.P. Saadat, T. Nies + 1 more
The modelbase package is a free expandable Python package for building and analysing dynamic mathematical models of biological systems. Originally it was designed for the simulation of metabolic systems, but it can be used for virtually any deterministic chemical processes. modelbase provides easy construction methods…
Authors not listed
Two kinetic schemes of the general modifier mechanism have been analysed in a quasi-steady state approximation, assuming that the reaction product concentration is negligible (a natural assumption for the initial rate method) and without additional simplifying assumptions. The characteristic equations have been…