In tnts paper,the Nonlinear Age-dependent forest evolution equation is discussed.The existence and uniqueness of the equation are have been proved.Also,we consider the equilibrium solution and nonequilibirium solution...In tnts paper,the Nonlinear Age-dependent forest evolution equation is discussed.The existence and uniqueness of the equation are have been proved.Also,we consider the equilibrium solution and nonequilibirium solution for the nonlinear forest systems with constant size,and give the necessary and sufficient conditions for the existence of equilibrium solution and nonequilibrium solution.展开更多
In recent years, integrated electricity-gas systems(IEGSs) have attracted widespread attention. The unifiedscheduling and control of the IEGS depends on high-precisionoperating data. To this end, it is necessary to es...In recent years, integrated electricity-gas systems(IEGSs) have attracted widespread attention. The unifiedscheduling and control of the IEGS depends on high-precisionoperating data. To this end, it is necessary to establish anappropriate state estimation (SE) model for IEGS to filter theraw measured data. Considering that power systems and naturalgas systems have different time scales and sampling periods, thispaper proposes a dynamic state estimation (DSE) method basedon a Kalman filter that can consider the dynamic characteristicsof natural gas pipelines. First, the standardized state transitionequations for the gas system are developed by applying the finitedifference method to the partial differential equations (PDEs) ofthe gas system;then the DSE model for IEGS is formulatedbased on a Kalman filter;also, the measurements from theelectricity system and the gas system with different samplingperiods are fused to ensure the observability of DSE by using theinterpolation method. The IEEE 39-bus electricity system and the18-nodes Belgium gas system are integrated as the test systems.Simulation results verify the proposed method’s accuracy andcalculation efficiency.展开更多
The derivation of nonlinear integrable evolution partial differential equations in higher dimensions has always been the holy grail in the field of integrability.The well-known modified Kd V equation is a prototypical...The derivation of nonlinear integrable evolution partial differential equations in higher dimensions has always been the holy grail in the field of integrability.The well-known modified Kd V equation is a prototypical example of an integrable evolution equation in one spatial dimension.Do there exist integrable analogs of the modified Kd V equation in higher spatial dimensions?In what follows,we present a positive answer to this question.In particular,rewriting the(1+1)-dimensional integrable modified Kd V equation in conservation forms and adding deformation mappings during the process allows one to construct higher-dimensional integrable equations.Further,we illustrate this idea with examples from the modified Kd V hierarchy and also present the Lax pairs of these higher-dimensional integrable evolution equations.展开更多
We consider matrix integrable fifth-order mKdV equations via a kind of group reductions of the Ablowitz–Kaup–Newell–Segur matrix spectral problems. Based on properties of eigenvalue and adjoint eigenvalue problems,...We consider matrix integrable fifth-order mKdV equations via a kind of group reductions of the Ablowitz–Kaup–Newell–Segur matrix spectral problems. Based on properties of eigenvalue and adjoint eigenvalue problems, we solve the corresponding Riemann–Hilbert problems, where eigenvalues could equal adjoint eigenvalues, and construct their soliton solutions, when there are zero reflection coefficients. Illustrative examples of scalar and two-component integrable fifthorder mKdV equations are given.展开更多
This paper aims to propose a fourth-order matrix spectral problem involving four potentials and generate an associated Liouville integrable hierarchy via the zero curvature formulation.A bi-Hamiltonian formulation is ...This paper aims to propose a fourth-order matrix spectral problem involving four potentials and generate an associated Liouville integrable hierarchy via the zero curvature formulation.A bi-Hamiltonian formulation is furnished by applying the trace identity and a recursion operator is explicitly worked out,which exhibits the Liouville integrability of each model in the resulting hierarchy.Two specific examples,consisting of novel generalized combined nonlinear Schrodinger equations and modified Korteweg-de Vries equations,are given.展开更多
文摘In tnts paper,the Nonlinear Age-dependent forest evolution equation is discussed.The existence and uniqueness of the equation are have been proved.Also,we consider the equilibrium solution and nonequilibirium solution for the nonlinear forest systems with constant size,and give the necessary and sufficient conditions for the existence of equilibrium solution and nonequilibrium solution.
基金This work was supported in part by National Natural Science Foundation of China(51777067)and(52077076)in part by funding from the State Key Laboratory of Alternate Electrical Power System with Renewable Energy Sources(LAPS2021-18).
文摘In recent years, integrated electricity-gas systems(IEGSs) have attracted widespread attention. The unifiedscheduling and control of the IEGS depends on high-precisionoperating data. To this end, it is necessary to establish anappropriate state estimation (SE) model for IEGS to filter theraw measured data. Considering that power systems and naturalgas systems have different time scales and sampling periods, thispaper proposes a dynamic state estimation (DSE) method basedon a Kalman filter that can consider the dynamic characteristicsof natural gas pipelines. First, the standardized state transitionequations for the gas system are developed by applying the finitedifference method to the partial differential equations (PDEs) ofthe gas system;then the DSE model for IEGS is formulatedbased on a Kalman filter;also, the measurements from theelectricity system and the gas system with different samplingperiods are fused to ensure the observability of DSE by using theinterpolation method. The IEEE 39-bus electricity system and the18-nodes Belgium gas system are integrated as the test systems.Simulation results verify the proposed method’s accuracy andcalculation efficiency.
基金sponsored by the National Natural Science Foundations of China(Nos.12235007,11975131,11435005,12275144,11975204)KC Wong Magna Fund in Ningbo UniversityNatural Science Foundation of Zhejiang Province No.LQ20A010009。
文摘The derivation of nonlinear integrable evolution partial differential equations in higher dimensions has always been the holy grail in the field of integrability.The well-known modified Kd V equation is a prototypical example of an integrable evolution equation in one spatial dimension.Do there exist integrable analogs of the modified Kd V equation in higher spatial dimensions?In what follows,we present a positive answer to this question.In particular,rewriting the(1+1)-dimensional integrable modified Kd V equation in conservation forms and adding deformation mappings during the process allows one to construct higher-dimensional integrable equations.Further,we illustrate this idea with examples from the modified Kd V hierarchy and also present the Lax pairs of these higher-dimensional integrable evolution equations.
基金supported in part by the National Natural Science Foundation of China (Grant Nos. 11975145, 11972291, and 51771083)the Ministry of Science and Technology of China (Grant No. G2021016032L)the Natural Science Foundation for Colleges and Universities in Jiangsu Province, China (Grant No. 17 KJB 110020)。
文摘We consider matrix integrable fifth-order mKdV equations via a kind of group reductions of the Ablowitz–Kaup–Newell–Segur matrix spectral problems. Based on properties of eigenvalue and adjoint eigenvalue problems, we solve the corresponding Riemann–Hilbert problems, where eigenvalues could equal adjoint eigenvalues, and construct their soliton solutions, when there are zero reflection coefficients. Illustrative examples of scalar and two-component integrable fifthorder mKdV equations are given.
基金supported in part by NSFC under Grants 12271488, 11975145 and 11972291the Ministry of Science and Technology of China (G2021016032L and G2023016011L)the Natural Science Foundation for Colleges and Universities in Jiangsu Province (17 KJB 110020)
文摘This paper aims to propose a fourth-order matrix spectral problem involving four potentials and generate an associated Liouville integrable hierarchy via the zero curvature formulation.A bi-Hamiltonian formulation is furnished by applying the trace identity and a recursion operator is explicitly worked out,which exhibits the Liouville integrability of each model in the resulting hierarchy.Two specific examples,consisting of novel generalized combined nonlinear Schrodinger equations and modified Korteweg-de Vries equations,are given.
