Classification of All Single Traveling Wave Solutions of Fractional Coupled Boussinesq Equations via the Complete Discrimination System Method

In this paper, the complete discrimination system method is used to construct the exact traveling wave solutions for fractional coupled Boussinesq equations in the sense of conformable fractional derivatives. As a result, we get the exact traveling wave solutions of fractional coupled Boussinesq equations, which include rational function solutions, Jacobian elliptic function solutions, implicit solutions, hyperbolic function solutions, and trigonometric function solutions. Finally, the obtained solution is compared with the existing literature.

Topological stability and patterns of traveling wave for a micro-polar non-Newtonian fluid model

A nonlinear micro-polar non-Newtonian fluid model is investigated. By the complete discrimination system for polynomial method, we give the classification of the traveling wave patterns and analysis of topological stability and dynamical behaviors. We also discuss the physical realizations and the conditions of existence of these patterns. As a result, when some of parameters are not intrinsic parameters we show that in general only two stable patterns will be observed.

New Exact Solutions of the Fractional Complex Ginzburg–Landau Equation

In this paper, we apply the complete discrimination system method to establish the exact solutions of the fractional complex Ginzburg–Landau equation in the sense of the conformable fractional derivative. Firstly, by the fractional traveling wave transformation, time-space fractional complex Ginzburg–Landau equation is reduced to an ordinary differential equation. Secondly, some new exact solutions are obtained by the complete discrimination system method of the three-order polynomial; these solutions include solitary wave solutions, rational function solutions, triangle function solutions, and Jacobian elliptic function solutions. Finally, two numerical simulations are imitated to explain the propagation of optical pulses in optic fibers. At the same time, the comparison between the previous results and our results are also given.

Exact Single Traveling Wave Solutions for Generalized Fractional Gardner Equations

In this paper, the classification of all single traveling wave solutions to generalized fractional Gardner equations is presented by utilizing the complete discrimination system method. Under the fractional traveling wave transformation, generalized fractional Gardner equations can be reduced to an ordinary differential equations. All possible exact traveling wave solutions are given through the complete discrimination system of the fourth-order polynomial. Moreover, graphical representations of different kinds of the exact solutions reveal that the method is of significance for searching the exact solutions to generalized fractional Gardner equations.

Exact Solutions to Zakharov-Kuznetsov Equation with Variable Coefficients by Trial Equation Method

By the trial equation method and the complete discrimination system for polynomial method, some exact solutions to Zakharov-Kuznetsov equation with variable coefficients are obtained. These solutions include solitary solutions, rational solutions, periodic solution and double periodic solutions.

Number of Forts in Iterated Logistic Mapping

Using the theory of complete discrimination system and the computer algebra systemMAPLE V.17, we compute the number of forts for the logistic mappingfλ(x)=λx(1-x)on[0,1]parameterized byλ∈(0,4]. We prove that if0<λ≤2then the number of forts does not increase under iteration and that ifλ>2then the number of forts is not bounded under iteration. Furthermore, we focus on the case ofλ>2and give for eachk=1,…,7some critical values ofλfor the change of numbers of forts.

Exact Travelling Wave Solutions for the Modified Fornberg-Whitham Equation

In this paper, by using the factorization technique combined with the method of complete discrimination system for polynomial, some exact travelling wave solutions for the modified Fornberg-Whitham equation are obtained. Moreover, our results extend previously known results in the literature.