On solitary wave solutions of a class of nonlinear partial differential equations based on the function<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:mrow><mml:mn>1</mml:mn><mml:mo>/</mml:mo><mml:msup><mml:mi>cosh</mml:mi><mml:mi>n</mml:mi></mml:msup><mml:mrow><mml:mo>(</mml:mo><mml:mi>α</mml:mi><mml:mi>x</mml:mi><mml:mo>+</mml:mo><mml:mi>β</mml:mi><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math>

Physica A: Statistical Mechanics and its Applications

2018

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We discuss a discrete-time model for motion of substance in a channel of a network. For the case of stationary motion of the substance and for the case of time-independent values of the parameters of the model we obtain a new class of statistical distributions that describe the distribution of the substance along the nodes of the channel. The case of interaction between a kind of substance specific for a node of the network and another kind of substance that is leaked from the channel is studied in presence of possibility for conversion between the two substances. Several scenarios connected to the dynamics of the two kinds of substances are described. The studied models: (i) model of motion of substance through a channel of a network, and (ii) model of interaction between two kinds of substances in a network node connected to the channel, are discussed from the point of view of human migration dynamics and interaction between the population of migrants and the native population of a country.

Section: Mathematical Formulation Of the Modelmentioning

confidence: 99%

Section: Mathematical Formulation Of the Modelmentioning

confidence: 99%

See 1 more Smart Citation

Discrete-time model for a motion of substance in a channel of a network with application to channels of human migration

Physica A: Statistical Mechanics and its Applications

2018

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AIP Conference Proceedings

“…Complex systems and their nonlinear dynamics are subject of many studies in the last decades [1] - [32] and many results have been obtained for the behavior and features of the dynamics of social and population complex systems [33] - [46]. In the last decades models of flows in networks are much used in the study of different kinds of problems, e.g, transportation problems [47]- [50].…”

Section: Introductionmentioning

confidence: 99%

Human migration: Model of a migration channel with a secondary and a tertiary arm

Borisov¹,

Vitanov²

2019

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We study the motion of substance in a finite channel that belongs to a network. The channel splits to two arms in a node of the network. There is an additional split of the secondary arm. We obtain analytical relationships for the distribution of the substance in the nodes of the channel for the case of stationary regime of the motion of the substance in the arms of the channel. The obtained results are discussed from the point of view of application of the model to migration dynamics: model of motion of migrants in a channel consisting of chains of countries with different probabilities for obtaining permission to stay for the migrants in the different countries of the channel

“…We note that the version called called Modified Method of Simplest Equation -MMSE [48], [49] based on determination of the kind of the simplest equation and truncation of the series of solutions of the simplest equation by means of application of a balance equation is equivalent of the Method of simplest equation. Up to now our contributions to the methodology and its application are connected to the MMSE [50] - [56]. We note especially the article [57] where we have extended the methodology of the MMSE to simplest equations of the class…”

Section: Introductionmentioning

confidence: 99%

Modified method of simplest equation for obtaining exact analytical solutions of nonlinear partial differential equations: further development of the methodology with applications

Dimitrova

Applied Mathematics and Computation

2015

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a b s t r a c tWe 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 trigonometric and hyperbolic functions as well as the elliptic function of Weierstrass and Jacobi. We show that for this case the studied class of nonlinear partial differential equations can be reduced to a system of two equations containing polynomials of the unknown functions. This system may be further reduced to a system of nonlinear algebraic equations for the parameters of the solved equation and parameters of the solution. Any nontrivial solution of the last system leads to a traveling wave solution of the solved nonlinear partial differential equation. The methodology is illustrated by obtaining solitary wave solutions for the generalized Korteweg-deVries equation and by obtaining solutions of the higher order Korteweg-deVries equation.