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Exact Solutions of Fisher and Generalized Fisher Equations with Variable Coefficients

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Acta Mathematicae Applicatae Sinica 2007年第4期23卷 563-568页

作者： Arzu ■ün Cevat Kart Department of Mathematics Faculty of SciencesAnkara University06100 Tando■an-Ankara Turkey

In this work, we consider a Fisher and generalized Fisher equations with variable coefficients. Using truncated painleve expansions of these equations, we obtain exact solutions of these equations with a constraint on... 详细信息

关键词： Nonlinear evolution equations fisher equation generalized fisher equation backlund transformation painleve property

Analysis of a population model with advection and an autocatalytic-type growth

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International Journal of Biomathematics 2023年第2期16卷 199-219页

作者： Valipuram Manoranjan Lewa'Alzaleq Department of Mathematics and Statistics Washington State University Pullman WA 99164USA Department of Mathematics Faculty of Science Alal-BaytUniversity Mafrag25113Jordan

This paper analyzes a population model with time-dependent advection and an autocatalytic-type *** opposed to a logistic growth where the rate of growth of the population decreases from the onset,an autocatalytic growth has a point of inflection where the rate of growth switches from an increasing trend to a decreasing *** the idea of painleve property,we show that a variety of exact traveling wave solutions can be obtained for this model depending on the choice of the advection *** particular,due to situations in resource distribution or environmental variations,if the advection is represented as a decaying function in time or an oscillating function in time,we are able to find exact solutions with interesting *** also carry out a computational study of the model using an exponentially upwinded numerical scheme and illustrate the movement of the solutions and their characteristics pictorially.

关键词： painleve property traveling wave solutions standing wave exponentially upwinded numerical scheme.

Painlev property of the modified C-KdV equation and its exact solutions

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Chinese Physics B 2010年第6期19卷 13-19页

作者：王惠董焕河王云虎王新赠 College of Information Science and Engineering Shandong University of Science and Technology

In this paper, the painleve properties of the modified C-KdV equation are verified by using the W-K algorithm. Then some exact soliton solutions are obtained by applying the standard truncated expansion method and the... 详细信息

关键词： painleve property standard truncated expansion nonstandard truncated expansion exact solution

A class of coupled nonlinear Schrdinger equations:Painlev'e property,exact solutions,and application to atmospheric gravity waves

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Applied Mathematics and Mechanics(English Edition) 2010年第11期31卷 1383-1404页

作者：刘萍李子良楼森岳 Department of Electronic Engineering University of Electronic Science and Technology of China Zhongshan Institute Department of Marine Meteorology Ocean University of China Department of Physics Shanghai Jiao Tong University Faculty of Science Ningbo University

The painleve integrability and exact solutions to a coupled nonlinear Schrodinger （CNLS） equation applied in atmospheric dynamics are discussed. Some parametric restrictions of the CNLS equation are given to pass the painleve test. Twenty periodic cnoidal wave solutions are obtained by applying the rational expansions of fundamental Jacobi elliptic functions. The exact solutions to the CNLS equation are used to explain the generation and propagation of atmospheric gravity waves.

关键词： coupled nonlinear SchrSdinger equation painleve property exact solution atmospheric gravity wave