Starting from a Backlund transformation and taking a special ansatz for the function f, we can obtain a much more generalexpression of solution that includes some variable separated functions for the higher-order Broe...Starting from a Backlund transformation and taking a special ansatz for the function f, we can obtain a much more generalexpression of solution that includes some variable separated functions for the higher-order Broer-Kaup system. From this expression, we investigate the interactions of localized coherent structures such as the multi-solitonic excitations and find the novel phenomenon that their interactions have non-elastic behavior because the fission/fusion may occur after the interaction of each localized coherent structure.展开更多
By using a Baecklund transformation and the multi-linear variable separationapproach, we find a new general solution of a (2+1)-dimensional generalization of the nonlinearSchroedinger system. The new 'universal...By using a Baecklund transformation and the multi-linear variable separationapproach, we find a new general solution of a (2+1)-dimensional generalization of the nonlinearSchroedinger system. The new 'universal' formula is defined, and then, rich coherent structures canbe found by selecting corresponding functions appropriately.展开更多
This paper is concerned with the oscillation of nonlinear partial difference equations with continuous variables and the corresponding dual equations. Several sufficientconditions are obtained for the oscillation of t...This paper is concerned with the oscillation of nonlinear partial difference equations with continuous variables and the corresponding dual equations. Several sufficientconditions are obtained for the oscillation of these equations.展开更多
Basing on the direct method developed by Clarkson and Kruskal, the nearly concentric Korteweg-de Vries （ncKdV） equation can be reduced to three types of （1＋1）-dimensional variable coefficients partial differentia...Basing on the direct method developed by Clarkson and Kruskal, the nearly concentric Korteweg-de Vries （ncKdV） equation can be reduced to three types of （1＋1）-dimensional variable coefficients partial differential equations （PDEs） and three types of variable coefficients ordinary differential equation. Furthermore, three types of （1＋1）-dimensional variable coefficients PDEs are all reduced to constant coefficients PDEs by some transformations.展开更多
A variable separation approach is used to obtain exact solutions of the (2+1)-dimensional generalized Nizhnik-Novikov-Veselov equation. Two of these exact solutions are analyzed to study the interaction between a line...A variable separation approach is used to obtain exact solutions of the (2+1)-dimensional generalized Nizhnik-Novikov-Veselov equation. Two of these exact solutions are analyzed to study the interaction between a line soliton and a y-periodic soliton (i.e. the array of the localized structure in the y direction, which propagates in the x direction) and between two dromions. The interactions between a line soliton and a y-periodic soliton are classified into several types according to the phase shifts due to collision. There are two types of singular interactions. One is the resonant interaction that generates one line soliton while the other is the extremely repulsive or long-range interaction where two solitons interchange each other infinitely apart. Some new phenomena of interaction between two dromions are also reported in this paper, and detailed behaviors of interactions are illustrated both analytically and graphically.展开更多
With more and more improvements of atmosphere or ocean models,a growing number of physical processes in the form of parameterization are incorporated into the models,which,on the one hand,makes the models capable of d...With more and more improvements of atmosphere or ocean models,a growing number of physical processes in the form of parameterization are incorporated into the models,which,on the one hand,makes the models capable of describing the at-mospheric or oceanic movement more precisely,and on the other hand,introduces non-smoothness in the form of "on-off" switches into the models."On-off" switches enhance the nonlinearity of the models and finally result in the loss of the effec-tiveness of variational data assimilation(VDA) based on the conventional adjoint method(ADJ).This study,in virtue of the optimization ability of a genetic algorithm(GA) for non-smooth problems,presents a new GA(referred to as GA NEW) to solve the problems of the VDA with discontinuous "on-off" processes.In the GA-NEW,adaptive selection and mutation oper-ators,blend crossover operator,and elitist strategy are combined in application.In order to verify the effectiveness and feasi-bility of the GA NEW in VDA,an idealized model of partial differential equation with discontinuous "on-off" switches in the forcing term is adopted as the governing equation.By comparison with the ADJ,it is shown that the GA NEW in VDA is more effective and can yield better assimilation retrievals.In addition,VDA experiments demonstrate that the performance of a GA is greatly related to the configuration of genetic operators(selection,crossover and mutation operators) and much better results may be attained with more proper genetic operations.Furthermore,the robustness of the GA NEW to observational noise,model errors and observation density is investigated,and the results show that the GA NEW has stronger robustness than the ADJ with respect to all the three observation noises,model errors,and sparse observation.展开更多
This paper studies the nonlinear variational inequality with integro-differential term arising from valuation of American style double barrier option. First, the authors use the penalty method to transform the variati...This paper studies the nonlinear variational inequality with integro-differential term arising from valuation of American style double barrier option. First, the authors use the penalty method to transform the variational inequality into a nonlinear parabolic initial boundary problem(i.e., penalty problem). Second, the existence and uniqueness of solution to the penalty problem are proved by using the Scheafer fixed point theory. Third, the authors prove the existence of variational inequality' solution by showing the fact that the penalized PDE converges to the variational inequality. The uniqueness of solution to the variational inequality is also proved by contradiction.展开更多
This paper is concerned with optimal harvesting control of a first order partial differential equation system representing a nonlinear n-dimensional competitive population model with age-structure. By the Ekeland＇s v...This paper is concerned with optimal harvesting control of a first order partial differential equation system representing a nonlinear n-dimensional competitive population model with age-structure. By the Ekeland＇s variational principle, the existence and unique char- acterization of the optimal control strategy are established. The optimality conditions for the control problem are obtained by the concept of the normal cone.展开更多
文摘Starting from a Backlund transformation and taking a special ansatz for the function f, we can obtain a much more generalexpression of solution that includes some variable separated functions for the higher-order Broer-Kaup system. From this expression, we investigate the interactions of localized coherent structures such as the multi-solitonic excitations and find the novel phenomenon that their interactions have non-elastic behavior because the fission/fusion may occur after the interaction of each localized coherent structure.
文摘By using a Baecklund transformation and the multi-linear variable separationapproach, we find a new general solution of a (2+1)-dimensional generalization of the nonlinearSchroedinger system. The new 'universal' formula is defined, and then, rich coherent structures canbe found by selecting corresponding functions appropriately.
基金Supported by the NSF of China(60174010)Supported by NSF of Hebei Province(102160)Supported by NS of Education Office in Heibei Province(2004123)
文摘This paper is concerned with the oscillation of nonlinear partial difference equations with continuous variables and the corresponding dual equations. Several sufficientconditions are obtained for the oscillation of these equations.
基金Supported by K.C. Wong Magna Fund in Ningbo University, NSF of China under Grant Nos. 10747141 and 10735030Zhejiang Provincial Natural Science Foundations of China under Grant No. 605408the Ningbo Natural Science Foundation under Grant Nos. 2007A610049 and 2006A610093
文摘Basing on the direct method developed by Clarkson and Kruskal, the nearly concentric Korteweg-de Vries （ncKdV） equation can be reduced to three types of （1＋1）-dimensional variable coefficients partial differential equations （PDEs） and three types of variable coefficients ordinary differential equation. Furthermore, three types of （1＋1）-dimensional variable coefficients PDEs are all reduced to constant coefficients PDEs by some transformations.
基金浙江省自然科学基金，浙江省宁波市博士基金，the State Kev Laboratory of Oil and Gas Reservoir Geology and Exploitation
文摘A variable separation approach is used to obtain exact solutions of the (2+1)-dimensional generalized Nizhnik-Novikov-Veselov equation. Two of these exact solutions are analyzed to study the interaction between a line soliton and a y-periodic soliton (i.e. the array of the localized structure in the y direction, which propagates in the x direction) and between two dromions. The interactions between a line soliton and a y-periodic soliton are classified into several types according to the phase shifts due to collision. There are two types of singular interactions. One is the resonant interaction that generates one line soliton while the other is the extremely repulsive or long-range interaction where two solitons interchange each other infinitely apart. Some new phenomena of interaction between two dromions are also reported in this paper, and detailed behaviors of interactions are illustrated both analytically and graphically.
基金supported by National Natural Science Foundation of China (Grant Nos.40975063 and 40830955)
文摘With more and more improvements of atmosphere or ocean models,a growing number of physical processes in the form of parameterization are incorporated into the models,which,on the one hand,makes the models capable of describing the at-mospheric or oceanic movement more precisely,and on the other hand,introduces non-smoothness in the form of "on-off" switches into the models."On-off" switches enhance the nonlinearity of the models and finally result in the loss of the effec-tiveness of variational data assimilation(VDA) based on the conventional adjoint method(ADJ).This study,in virtue of the optimization ability of a genetic algorithm(GA) for non-smooth problems,presents a new GA(referred to as GA NEW) to solve the problems of the VDA with discontinuous "on-off" processes.In the GA-NEW,adaptive selection and mutation oper-ators,blend crossover operator,and elitist strategy are combined in application.In order to verify the effectiveness and feasi-bility of the GA NEW in VDA,an idealized model of partial differential equation with discontinuous "on-off" switches in the forcing term is adopted as the governing equation.By comparison with the ADJ,it is shown that the GA NEW in VDA is more effective and can yield better assimilation retrievals.In addition,VDA experiments demonstrate that the performance of a GA is greatly related to the configuration of genetic operators(selection,crossover and mutation operators) and much better results may be attained with more proper genetic operations.Furthermore,the robustness of the GA NEW to observational noise,model errors and observation density is investigated,and the results show that the GA NEW has stronger robustness than the ADJ with respect to all the three observation noises,model errors,and sparse observation.
基金supported by the National Science Foundation of China under Grant Nos.71171164 and 70471057the Doctorate Foundation of Northwestern Polytechnical University under Grant No.CX201235
文摘This paper studies the nonlinear variational inequality with integro-differential term arising from valuation of American style double barrier option. First, the authors use the penalty method to transform the variational inequality into a nonlinear parabolic initial boundary problem(i.e., penalty problem). Second, the existence and uniqueness of solution to the penalty problem are proved by using the Scheafer fixed point theory. Third, the authors prove the existence of variational inequality' solution by showing the fact that the penalized PDE converges to the variational inequality. The uniqueness of solution to the variational inequality is also proved by contradiction.
文摘This paper is concerned with optimal harvesting control of a first order partial differential equation system representing a nonlinear n-dimensional competitive population model with age-structure. By the Ekeland＇s variational principle, the existence and unique char- acterization of the optimal control strategy are established. The optimality conditions for the control problem are obtained by the concept of the normal cone.
