In this work, we apply the bifurcation method of dynamical systems to investigate the underlying complex dynamics of traveling wave solutions to a highly nonlinear Fujimoto–Watanabe equation. We identify all bifurcat...In this work, we apply the bifurcation method of dynamical systems to investigate the underlying complex dynamics of traveling wave solutions to a highly nonlinear Fujimoto–Watanabe equation. We identify all bifurcation conditions and phase portraits of the system in different regions of the three-dimensional parametric space, from which we present the sufficient conditions to guarantee the existence of traveling wave solutions including solitary wave solutions, periodic wave solutions, kink-like(antikink-like) wave solutions, and compactons. Furthermore, we obtain their exact expressions and simulations, which can help us understand the underlying physical behaviors of traveling wave solutions to the equation.展开更多
Let W =(W_t)_(t≥0) be a supercritical a-stable Dawson-Watanabe process(withα∈(0,2]) and f be a test function in the domain of-(-△)^(α/2) satisfying some integrability condition. Assuming the initial measure W_0 h...Let W =(W_t)_(t≥0) be a supercritical a-stable Dawson-Watanabe process(withα∈(0,2]) and f be a test function in the domain of-(-△)^(α/2) satisfying some integrability condition. Assuming the initial measure W_0 has a finite positive moment, we determine the long-time asymptotic of arbitrary order of W_t(f). In particular, it is shown that the local behavior of Wt in long-time is completely determined by the asymptotic of the total mass W_t(1), a global characteristic.展开更多
We study dynamical behaviors of traveling wave solutions to a Fujimoto-Watanabe equation using the method of dynamical systems. We obtain all possible bifurcations of phase portraits of the system in different regions...We study dynamical behaviors of traveling wave solutions to a Fujimoto-Watanabe equation using the method of dynamical systems. We obtain all possible bifurcations of phase portraits of the system in different regions of the threedimensional parameter space. Then we show the required conditions to guarantee the existence of traveling wave solutions including solitary wave solutions, periodic wave solutions, kink-like(antikink-like) wave solutions, and compactons. Moreover, we present exact expressions and simulations of these traveling wave solutions. The dynamical behaviors of these new traveling wave solutions will greatly enrich the previews results and further help us understand the physical structures and analyze the propagation of nonlinear waves.展开更多
假设复句是现代汉语语法体系中不可或缺的句子类型之一,在翻译成维吾尔语时,受语境和表达规则的限制,有时保持原句结构,有时灵活采用符合维吾尔语表达习惯的方式处理。本文在前人理论基础上探究汉语假设复句的句法特征及其在维吾尔语中...假设复句是现代汉语语法体系中不可或缺的句子类型之一,在翻译成维吾尔语时,受语境和表达规则的限制,有时保持原句结构,有时灵活采用符合维吾尔语表达习惯的方式处理。本文在前人理论基础上探究汉语假设复句的句法特征及其在维吾尔语中的对应表达方式,旨在用维吾尔语表达汉语假设复句时,既能在意义上与汉语保持一致,又能在形式上体现风格。 The hypothetical complex sentence is one of the indispensable sentence types in modern Chinese grammar system. When translated into Uyghur language, it is limited by context and expression rules, sometimes it can maintain the original sentence structure, but sometimes it is flexibly dealt with the expression habits of Uyghur language. On the basis of previous theories, this paper explores the syntactic characteristics of Chinese hypothetical complex sentences and their corresponding expressions in Uygur. We hope when expressing Chinese hypothesis complex sentences in Uyghur, it can not only be consistent with Chinese in the sense, but also reflect the style in the form.展开更多
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11701191 and 11871232)the Program for Innovative Research Team in Science and Technology in University of Fujian Province,Quanzhou High-Level Talents Support Plan(Grant No.2017ZT012)the Subsidized Project for Cultivating Postgraduates’ Innovative Ability in Scientific Research of Huaqiao University
文摘In this work, we apply the bifurcation method of dynamical systems to investigate the underlying complex dynamics of traveling wave solutions to a highly nonlinear Fujimoto–Watanabe equation. We identify all bifurcation conditions and phase portraits of the system in different regions of the three-dimensional parametric space, from which we present the sufficient conditions to guarantee the existence of traveling wave solutions including solitary wave solutions, periodic wave solutions, kink-like(antikink-like) wave solutions, and compactons. Furthermore, we obtain their exact expressions and simulations, which can help us understand the underlying physical behaviors of traveling wave solutions to the equation.
文摘Let W =(W_t)_(t≥0) be a supercritical a-stable Dawson-Watanabe process(withα∈(0,2]) and f be a test function in the domain of-(-△)^(α/2) satisfying some integrability condition. Assuming the initial measure W_0 has a finite positive moment, we determine the long-time asymptotic of arbitrary order of W_t(f). In particular, it is shown that the local behavior of Wt in long-time is completely determined by the asymptotic of the total mass W_t(1), a global characteristic.
基金Project supported by the National Natural Science Foundation of China(Grant No.11701191)Subsidized Project for Cultivating Postgraduates’ Innovative Ability in Scientific Research of Huaqiao University,China
文摘We study dynamical behaviors of traveling wave solutions to a Fujimoto-Watanabe equation using the method of dynamical systems. We obtain all possible bifurcations of phase portraits of the system in different regions of the threedimensional parameter space. Then we show the required conditions to guarantee the existence of traveling wave solutions including solitary wave solutions, periodic wave solutions, kink-like(antikink-like) wave solutions, and compactons. Moreover, we present exact expressions and simulations of these traveling wave solutions. The dynamical behaviors of these new traveling wave solutions will greatly enrich the previews results and further help us understand the physical structures and analyze the propagation of nonlinear waves.
文摘假设复句是现代汉语语法体系中不可或缺的句子类型之一,在翻译成维吾尔语时,受语境和表达规则的限制,有时保持原句结构,有时灵活采用符合维吾尔语表达习惯的方式处理。本文在前人理论基础上探究汉语假设复句的句法特征及其在维吾尔语中的对应表达方式,旨在用维吾尔语表达汉语假设复句时,既能在意义上与汉语保持一致,又能在形式上体现风格。 The hypothetical complex sentence is one of the indispensable sentence types in modern Chinese grammar system. When translated into Uyghur language, it is limited by context and expression rules, sometimes it can maintain the original sentence structure, but sometimes it is flexibly dealt with the expression habits of Uyghur language. On the basis of previous theories, this paper explores the syntactic characteristics of Chinese hypothetical complex sentences and their corresponding expressions in Uygur. We hope when expressing Chinese hypothesis complex sentences in Uyghur, it can not only be consistent with Chinese in the sense, but also reflect the style in the form.