Considered here is the stability problem of solitary traveling waves with non-zero boundary of an equation describing the free surface waves of moderate amplitude in the shallow water regime. We employ a transform to convert the stability problem of solitary waves with non-zero boundary to the same one of solitary waves vanishing at infinity for a new equation, such that the abstract stability theorem proposed by Grillakis et al. can work on it. We then show that the solitary traveling waves with non-zero boundary are orbitally stable under certain parameter conditions.
We consider the nonlinear dynamics in a double-chain model of DNA which consists of two long elastic homogeneous strands connected with each other by an elastic membrane. By using the method of dynamical systems, the bounded traveling wave solutions such as bell-shaped solitary waves and periodic waves for the coupled nonlinear dynamical equations of DNA model are obtained and simulated numerically. For the same wave speed, bell-shaped solitary waves of different heights are found to coexist.
In this paper, we investigate the relationship between the weak min-max property and the diameter uniformity of domains in Banach spaces with dimension at least 2. As an application, we show that diameter uniform domains are invariant under relatively quasimöbius mappings.
Abstract In this paper we study the Boussinesq equation with power law nonlinearity and dual dispersion which arises in fluid dynamics. A particular kind of product of distributions is introduced and applied to solve non-smooth solutions of this equation. It is proved that, under certain conditions, a distribution solution as a singular Dirac delta function exists for this model. For the first time, this kind of product of distributions is used to deal with a fourth order nonlinear partial differential equation.
The establishment of the professional degree of master of education has opened up a channel for Chinese primary and secondary school teachers to obtain graduate degrees.It has developed extremely rapidly since the official enrollment, and it has become an important part of degree and graduate education in China.It has trained a large number of backbone teachers and excellent managers for basic education in China.Although the development of master of education in China shows a good development trend, due to the large number of people involved in basic education, the cultivation of master of education in China is still in a period of continuous construction, which does not fully meet the actual needs in terms of quantity and quality.Therefore, professional master education is still hovering at the door of possibility research and feasibility exploration, and it is difficult for master of education to enter the operable practice hall of basic education to show their skills.Thus, the society questions the applicability of master of education more or less.In order to cultivate the professional master of mathematics better, it is necessary to implement a comprehensive reform of the talent training program for the graduate students of mathematics major, and establish a joint training mechanism for the graduate students of mathematics education from three aspects: colleges and universities (Foshan University), local education bureau, and primary and secondary schools.Based on the above reasons, this paper will carry out further research on the talent training mode of master of mathematics education in our college, and strive to make a breakthrough.A number of theoretical and practical achievements in the cultivation of master of mathematics education talents in local universities have been formed to provide reference for the construction of professional and master education system in Guangdong and China.
We consider the orbital stability of solitary traveling wave solutions of an equation describing the free surface waves of moderate amplitude in the shallow water regime. Firstly, we rewrite this equation in Hamiltonian form and construct two invariants of motion. Then using the abstract stability theorem of solitary waves proposed by Grillakis et al. (1987), we prove that the solitary traveling waves of the equation under consideration are orbital stable.
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