In the interaction of laser-plasma the system of Zakharov equation plays an important role.This system attracted many scientists' wide interest and attention.And the formation, evolution and interaction of the Lan...In the interaction of laser-plasma the system of Zakharov equation plays an important role.This system attracted many scientists' wide interest and attention.And the formation, evolution and interaction of the Langmuir solutions differ from solutions of the KDV equation. Here we consider the following generalized Zakharov展开更多
In this paper, we look for solutions to the following Schrödinger-Bopp-Podolsky system with prescribed L<sup>2</sup>-norm constraint , where q ≠ 0, a, ρ> 0 are constants. At firs...In this paper, we look for solutions to the following Schrödinger-Bopp-Podolsky system with prescribed L<sup>2</sup>-norm constraint , where q ≠ 0, a, ρ> 0 are constants. At first, by the classical minimizing argument, we obtain a ground state solution to the above problem for sufficiently small ρwhen . Secondly, in the case p = 6, we show the nonexistence of positive solutions by using a Liouville-type result. Finally, we argue by contradiction to investigate the orbital stability of standing waves for .展开更多
We prove that the two-component peakon solutions are orbitally stable in the energy space.The system concerned here is a two-component Novikov system,which is an integrable multi-component extension of the integrable ...We prove that the two-component peakon solutions are orbitally stable in the energy space.The system concerned here is a two-component Novikov system,which is an integrable multi-component extension of the integrable Novikov equation.We improve the method for the scalar peakons to the two-component case with genuine nonlinear interactions by establishing optimal inequalities for the conserved quantities involving the coupled structures.Moreover,we also establish the orbital stability for the train-profiles of these two-component peakons by using the refined analysis based on monotonicity of the local energy and an induction method.展开更多
In this paper, we study the existence of standing waves for the nonlinear Schrödinger equation with combined power-type nonlinearities and a partial harmonic potential. In the L<sup>2</sup>-supercriti...In this paper, we study the existence of standing waves for the nonlinear Schrödinger equation with combined power-type nonlinearities and a partial harmonic potential. In the L<sup>2</sup>-supercritical case, we obtain the existence and stability of standing waves. Our results are complements to the results of Carles and Il’yasov’s artical, where orbital stability of standing waves have been studied for the 2D Schrödinger equation with combined nonlinearities and harmonic potential.展开更多
Based on the mechanism of prevention and control of infectious disease, we propose, in this paper, an SIRS epidemic model with varying total population size and state-dependent control, where the fraction of susceptib...Based on the mechanism of prevention and control of infectious disease, we propose, in this paper, an SIRS epidemic model with varying total population size and state-dependent control, where the fraction of susceptible individuals in population is as the detection threshold value. By the Poincaré map, theory of differential inequalities and differential equation geometry, the existence and orbital stability of the disease-free periodic solution are discussed. Theoretical results show that by state-dependent pulse vaccination we can make the proportion of infected individuals tend to zero, and control the transmission of disease in population.展开更多
基金The research is supported by the Scientific Research Foundation of Yunnan Provincial Departmentthe Natural Science Foundation of Yunnan Province(No.2005A0026M).
文摘In the interaction of laser-plasma the system of Zakharov equation plays an important role.This system attracted many scientists' wide interest and attention.And the formation, evolution and interaction of the Langmuir solutions differ from solutions of the KDV equation. Here we consider the following generalized Zakharov
文摘In this paper, we look for solutions to the following Schrödinger-Bopp-Podolsky system with prescribed L<sup>2</sup>-norm constraint , where q ≠ 0, a, ρ> 0 are constants. At first, by the classical minimizing argument, we obtain a ground state solution to the above problem for sufficiently small ρwhen . Secondly, in the case p = 6, we show the nonexistence of positive solutions by using a Liouville-type result. Finally, we argue by contradiction to investigate the orbital stability of standing waves for .
基金National Natural Science Foundation of China(Grants Nos.12271424 and 11871395)National Natural Science Foundation of China(Grants Nos.11971251,11631007 and 12111530003)。
文摘We prove that the two-component peakon solutions are orbitally stable in the energy space.The system concerned here is a two-component Novikov system,which is an integrable multi-component extension of the integrable Novikov equation.We improve the method for the scalar peakons to the two-component case with genuine nonlinear interactions by establishing optimal inequalities for the conserved quantities involving the coupled structures.Moreover,we also establish the orbital stability for the train-profiles of these two-component peakons by using the refined analysis based on monotonicity of the local energy and an induction method.
文摘In this paper, we study the existence of standing waves for the nonlinear Schrödinger equation with combined power-type nonlinearities and a partial harmonic potential. In the L<sup>2</sup>-supercritical case, we obtain the existence and stability of standing waves. Our results are complements to the results of Carles and Il’yasov’s artical, where orbital stability of standing waves have been studied for the 2D Schrödinger equation with combined nonlinearities and harmonic potential.
文摘Based on the mechanism of prevention and control of infectious disease, we propose, in this paper, an SIRS epidemic model with varying total population size and state-dependent control, where the fraction of susceptible individuals in population is as the detection threshold value. By the Poincaré map, theory of differential inequalities and differential equation geometry, the existence and orbital stability of the disease-free periodic solution are discussed. Theoretical results show that by state-dependent pulse vaccination we can make the proportion of infected individuals tend to zero, and control the transmission of disease in population.
