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Title: Multi-integrable couplings with Hamiltonian structures Speaker: Wen-Xiu Ma Time: 4:00pm‐5:00pm Place: CHE 302
We will discuss how to generate multi-integrable couplings, particularly bi-integrable or tri-integrable couplings. The starting point is non-semisimple Lie algebras consisting of block matrices. Variational identities will be tools for furnishing Hamiltonian structures.
Title: Reliable analysis for exact solutions of nonlinear Schrödinger equations Speaker: Ahmet Yildirim, Ege University Turkey Time: 4:00pm‐5:00pm Place: CHE 302
In this talk, we consider a few of nonlinear Schrödinger equations. A direct method will be presented to construct exact solutions to those nonlinear Schrödinger equations. Our examples will show that the approach is powerful in generating exact solutions to nonlinear partial differential equations, including non-integrable equations.
Title: Discussion on the multiple exp-function method and its application to the potential-YTSF equation Speaker: Arbin Rai Time: 4:00pm‐5:00pm Place: CHE 302
In this talk, I will discuss the multiple exp-function method for exact multiple wave solutions of nonlinear partial differential equations. With the help of Maple, an application to the \((3+1)\)-dimensional potential Yu-Toda-Sasa-Fukuyama equation yields exact explicit one-wave, two-wave, and three-wave solutions, including one-soliton, two-soliton and three-soliton type solutions.
Title: A brief introduction to the homogenous balance method Speaker: Hui-Qun Zhang, Qingdao University PR China Time: 4:00pm‐5:00pm Place: CHE 302
We would like to give a brief introduction to the homogenous balance method, including its solving process and abundant applications.
Title: Pfaffian and Wronskian solutions in \(3+1\) dimensions Speaker: Magdy G. Asaad Time: 4:00pm‐5:00pm Place: CHE 302
In this talk, I will present our recent work on various classes of Pfaffian and Wronskian solutions to a class of generalized integrable nonlinear partial differential equations, including soliton equations, in three spatial and one temporal dimensions. Solitons are among the most beneficial solutions for science and technology, from ocean waves to transmission of information through optical fibers or energy transport along protein molecules. As part of this talk, I will show how to obtain \(N\)-soliton solutions from the Pfaffian and Wronskian solutions.
Title: A study of Kawahara equation in weighted Sobolev spaces Speaker: Netra Khanal, University of Tampa Time: 4:00pm‐5:00pm Place: CHE 302
The initial- and boundary-value problem for the Kawahara equation, a fifth-order KdV type equation, will be discussed in weighted Sobolev spaces. The theory presented includes the existence and uniqueness of a local mild solution and of a global strong solution in these weighted spaces. If the \(L^2\)-norm of the initial data is sufficiently small, these solutions decay exponentially in time.
Title: The variational iteration method: An efficient scheme for handling fractional partial differential equations in fluid mechanics Speaker: Ms. Canan Unlu, Istanbul University Turkey Time: 4:00pm‐5:00pm Place: CHE 302
We will discuss the variational iteration method and its applications. A general framework will be presented for analytical treatment of fractional partial differential equations in fluid mechanics. Numerical illustrations will be given to show the pertinent features of the technique.
Title: Polyvector fields and Lie derivatives Speaker: Hongchan Zheng, Northwestern Polytechnical University China Time: 4:00pm‐5:00pm Place: CHE 302
We will discuss \(k\)-vector fields and the Lie derivative operation, including properties of the Lie derivative and the relationship between the Lie derivative and the Lie bracket. We will show also how the Lie derivative can be extended to differential \(k\)-forms and how one can build its applications.
Title: Differential forms and polyvector fields on manifolds Speaker: Hongchan Zheng, Northwestern Polytechnical University China Time: 4:00pm‐5:00pm Place: CHE 302
We will discuss the differential \(k\)-forms and \(k\)-vector fields on differentiable manifolds and the operations on and between them, including the basic properties of the wedge product and the exterior derivative.
Title: A brief review of models in mosquito control Speaker: Prof. Nanhua Zhang, USF College of Public Health Time: 4:00pm‐5:00pm Place: CHE 302
It is well known that mosquitoes transmit many infectious diseases (malaria, West Nile fever, Rift Valley fever, etc.) and there have been tremendous efforts to reduce their presence. Mathematical models are useful in guiding these mosquito control efforts. In this talk, I will review some models in mosquito control. I will introduce some unsolved problems that deserve attention from applied mathematicians.
Title: Integrable couplings of the Kaup-Newell hierarchy Speaker: Mengshu Zhang Time: 4:00pm‐5:00pm Place: CHE 302
We will discuss integrable couplings of soliton equations. As an example, we will present a hierarchy of integrable couplings for the Kaup-Newell soliton equations by using zero curvature equations.
Title: Bi-integrable couplings and their Hamiltonian structures Speaker: Jinghan Meng Time: 4:00pm‐5:00pm Place: CHE 302
We will present our recent research on bi-integrable couplings of soliton equations. Hamiltonian structures of the bi-integrable coupling hierarchies are established by means of the component trace identity, which generate infinitely many commuting symmetries and conservation laws. Illustrative examples will be given.
Title: Distributions and the Frobenius Theorem Speaker: Junyi Tu Time: 4:00pm‐5:00pm Place: CHE 302
We would like to discuss some basic structures on real smooth manifolds, including the canonical form of vector fields near a regular point, and the generalization of this idea to higher-dimensional sub-manifolds, which is the content of the Frobenius Theorem.