The goal of this article is to discuss the Simple Equations Method (SEsM) for obtaining exact solutions nonlinear partial differential equations and show that several well-known methods such are connected SEsM. In more detail, we Hirota method a particular case SEsM specific form function from Step 2 simple kinds exponential functions. We illustrate by three- soliton solution Korteweg-de Vries equation, two-soliton Schrödinger Ishimori equation spin dynamics ferromagnetic materials. Then can...

Abstract We consider an extension of the methodology modified method simplest equation to case use two equations. The extended is applied for obtaining exact solutions model nonlinear partial differential equations deep water waves: Schrödinger equation. It shown that works also other kind.

We discuss a method for obtaining exact solutions of nonlinear partial differential equations called the Simple Equations Method (SEsM) which is based on representation searched solution as function one or several simple equations. describe methodology and show that SEsM contains particular case Modified Simplest Equation, G'/G - method, Exp-function Tanh-method Fourier series approximate linear These methods are only small parts cases SEsM.

We discuss the Simple Equations Method (SEsM) for obtaining exact solutions of nonlinear partial differential equations. show that Hirota method is particular case SEsM specific form function from Step. 2 and simple equations kind equation exponential function. illustrate methodology by three-soliton solution Korteweg - de Vries equation, two soliton Schrödinger Ishimori spin dynamics ferromagnetic materials.

We discuss the Simple Equations Method (SEsM) for obtaining exact solutions of nonlinear partial differential equations. show that Jacobi Elliptic Function Expansion Method, F-Expansion method, Modified Equation Trial General Projective Riccati and First Integral are specific cases SEsM.

Abstract The concept of "primacy" as introduced by Jefferson in 1939 urban geography leads to the notion "dominant city" also known primate city. Practically, was extended Sheppard view discussing some "hierarchy". type dominance is not universal nor any hierarchy reversal. Both can be time and sample dependent. Thus, an example taking into consideration existence both pieces puzzle, we consider discuss Bulgarian system. It interesting compare data on two groups cities different intervals:...

We discuss the Simple Equations Method (SEsM) for obtaining exact solutions of a class nonlinear differential equations containing polynomial nonlinearities. present an amended version methodology, which is based on use composite functions. The number steps SEsM was reduced from seven to four in methodology. For case with nonlinearities, can reduce solved system algebraic equations. Each nontrivial solution this leads prove theorems and examples functions methodology following three kinds...

The focus of this presentation is on the application Simple Equations Method (SEsM) for obtaining exact solutions nonlinear differential equations. We discuss several examples based last developments methodology. goal to illustrate results from derivatives composite functions in algorithm SEsM. are connected with which two simple functions. These Jacobi elliptic and their specific cases: trigonometric hyperbolic

Abstract We investigate flow of incompressible fluid in a cylindrical tube with elastic walls. The radius the may change along its length. discussed problem is connected to fluid-structure interaction large human arteries and especially nonlinear effects. long-wave approximation applied solve model equations. obtained Korteweg-deVries equation possessing variable coefficient reduced dynamical system three first order differential low probability solitary wave arising shown. Periodic...

We discuss propagation of traveling waves in a blood-filled hyper–elastic artery with local dilatation (an aneurysm). The processes the injured are modeled by an equation motion arterial wall and equations fluid (the blood). Taking into account specific geometry applying reductive perturbation method long-wave approximation we reduce model to version perturbed Korteweg-de Vries kind variable coefficients. Exact traveling-wave solutions this obtained modified simplest where differential Abel...