An upper order bound of the invariant manifold in Lax pairs of a nonlinear evolution partial differential equation

Zhang, Zhiyong

doi:10.1088/1751-8121/ab224e

Cited by 5 publications

(3 citation statements)

References 16 publications

(49 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Where, L represents the logistics cost under the e-commerce mode; E represents the constant in the logistics parameters to be estimated; The meanings of other variables are the same as those in equation ( 8) [18][19]. Suppose Company A is selected as an example, experts are used to estimate the sales volume of each marketing mix, and the variable data of estimated sales volume, commodity price, advertising cost, design maintenance cost, logistics cost and other factors are substituted into Formula (9) for OLS estimation.…”

Section: Application Analysis Of Marketing Function Under E-commerce ...mentioning

confidence: 99%

Application of Nonlinear Differential Equation in Electronic Commerce

Xiao

2023

Applied Mathematics and Nonlinear Sciences

View full text Add to dashboard Cite

The author analyzes the network marketing model under the e-commerce mode through the marketing function under the nonlinear differential equation, through the research, it is found that the four variables of commodity price, advertising investment, sales model design investment and logistics investment are the key explanatory variables of sales volume of marketing network, among them, the price of goods has the greatest impact on online marketing, secondly, advertising investment, logistics investment and design investment have less impact.

show abstract

Section: Application Analysis Of Marketing Function Under E-commerce ...mentioning

confidence: 99%

Application of Nonlinear Differential Equation in Electronic Commerce

Xiao

2023

Applied Mathematics and Nonlinear Sciences

View full text Add to dashboard Cite

show abstract

“…Sometimes the problem of determining orders causes problems. The corresponding relationship between these two orders for the case of equations of the KdV type was established in [20].…”

Section: Introductionmentioning

confidence: 99%

Invariant manifolds and separation of the variables for integrable chains

Habibullin¹,

Khakimova²

2020

J. Phys. A: Math. Theor.

View full text Add to dashboard Cite

A notion of the generalized invariant manifold for a nonlinear integrable lattice is considered. Earlier, it has been observed that this kind of objects provide an effective tool for evaluating the recursion operators and Lax pairs. In this article we show with an example of the Volterra chain that the generalized invariant manifold can be used for constructing exact particular solutions as well. To this end we first find an invariant manifold depending on two constant parameters. Then we assume that an ordinary difference equation (ODE) defining the generalized invariant manifold has a solution polynomially depending on one of the spectral parameters and derive an ODE, for the roots of the polynomials. The efficiency of the method is approved by some illustrative examples.

show abstract

“…The purpose of the article is to show that this nonlinear Lax pair can be used for constructing explicit solutions of the equation (2). Recently Zhang Zhi-Yong has observed some useful properties of the generalized invariant manifolds (see [18]).…”

Section: Introductionmentioning

confidence: 99%

Invariant manifolds and Lax pairs for integrable nonlinear chains

Habibullin

Khakimova

2017

Theor Math Phys

View full text Add to dashboard Cite

A notion of the generalized invariant manifold for a nonlinear integrable lattice is considered. Earlier it has been observed that this kind objects provide an effective tool for evaluating the recursion operators and Lax pairs. In this article we show with an example of the Volterra chain that the generalized invariant manifold can be used for constructing exact particular solutions as well. To this end we first find an invariant manifold depending on two constant parameters. Then we assume that ordinary difference equation defining the generalized invariant manifold has a solution polynomially depending on one of the spectral parameters and derive ordinary difference and differential equations, for the roots of the polynomials. In the simplest nontrivial case we constructed exact common solutions to these equations. As a result we derived for the Volterra chain a new explicit solution, displaying unusual behavior.

show abstract

An upper order bound of the invariant manifold in Lax pairs of a nonlinear evolution partial differential equation

Cited by 5 publications

References 16 publications

Application of Nonlinear Differential Equation in Electronic Commerce

Application of Nonlinear Differential Equation in Electronic Commerce

Invariant manifolds and separation of the variables for integrable chains

Invariant manifolds and Lax pairs for integrable nonlinear chains

Contact Info

Product

Resources

About