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Multi-Soliton Solutions To A Model Equation For Shallow Water Waves, Zhijiang Qiao
Multi-Soliton Solutions To A Model Equation For Shallow Water Waves, Zhijiang Qiao
Theses and Dissertations - UTB/UTPA
In Soliton theory, Hirota direct method is most efficient tool for seeking one soliton solutions or multi-soliton solutions of integrable nonlinear partial differential equations. The key step of the Hirota direct method is to transform the given equation into its Hirota bilinear form. Once the bilinear form of the given equation is found, we can construct the soliton and multi-soliton solutions of that model. Many interesting characteristics of Pfaffians were discovered through studies of soliton equations. In this thesis, a shallow water wave model and its bilinear equation are investigated. Using Hirota direct method, we obtain the multi-soliton solutions and …
Identification Of Parameters And The Distribution Of The Maximum And The Minimum, Lijuan Bi
Identification Of Parameters And The Distribution Of The Maximum And The Minimum, Lijuan Bi
Theses and Dissertations - UTB/UTPA
In problems of competing risks, where an individual may be subject to m causes of death and X(i) is the lifetime of an individual exposed to the ith cause, the X(i)s are not observable but only is their minimum, and inference is needed on the X(i) based on their minimum. The same is the case with a m-component system, where the components are connected in series, and we are interested in inference on the lifetimes of the individual components. These examples motivate problems on parameter identification by the distribution of the minimum. Similarly, the example of a m-component system where …
Duffing-Van Der Pol Type Oscillator, Guangyue Gao
Duffing-Van Der Pol Type Oscillator, Guangyue Gao
Theses and Dissertations - UTB/UTPA
The nonlinear Duffing-van der Pol oscillator system is studied by means of the Lie symmetry reduction method and the Preller-Singer method. With the particular case of coefficients, this system has physical relevance as a simple model in certain flow-induced structural vibration problems. Under certain parametric conditions, we are concerned with the first integrals of the Duffing-van der Pol oscillator system. After making a series of variable transformations, we apply the Preller-Singer method and the Lie symmetry reduction method to obtain the first integrals of the simplified equations without complicated calculations.
Modeling Instabilities Of Electrically Driven Jets With Finite Conductivity Under Constant Or Variable Applied Field, Saulo I. Orizaga
Modeling Instabilities Of Electrically Driven Jets With Finite Conductivity Under Constant Or Variable Applied Field, Saulo I. Orizaga
Theses and Dissertations - UTB/UTPA
We investigate the problem of spatial (S), combined spatial and temporal (CST), and non-linear temporal instability (NLT) of electrically driven viscous jets with finite electrical conductivity and in the presence of either a constant or a variable applied electric field. A mathematical model, which is developed and used for the spatially growing disturbances in electrically driven jet flows, leads to a lengthy equation for the unknown growth rate and frequency of the disturbances. This equation is solved numerically using Newton‟s Method. For neutral temporal stability boundary, we find, in particular, two new spatial modes of instability under certain conditions. One …
Soliton Solutions To Integrable Equations, Haiqi Wang
Soliton Solutions To Integrable Equations, Haiqi Wang
Theses and Dissertations - UTB/UTPA
In recent years, integrable systems and soliton theory play an important role in the study of nonlinear water wave equations. In this thesis, we will focus on the procedure of how to get soliton solutions for integrable equations. The fundamental idea is to use the traveling wave setting to convert a partial differential equation to an ordinary differential equation and to solve ordinary differential equations yields soliton solutions for the integrable equations under certain boundary conditions at both negative and positive infinities. In our work, we will consider five integrable equations and present their solitons solutions, one of which will …