We analytically give the financial rogue waves in the nonlinear option pricing model due to Ivancevic,which is nonlinear wave alternative of the Black-Scholes model.These rogue wave solutions may be used to describe t...We analytically give the financial rogue waves in the nonlinear option pricing model due to Ivancevic,which is nonlinear wave alternative of the Black-Scholes model.These rogue wave solutions may be used to describe thepossible physical mechanisms for rogue wave phenomenon in financial markets and related fields.展开更多
In this paper, a Ritt-Wu＇s characteristic set method for ordinary difference systems is proposed, which is valid for any admissible ordering. New definition for irreducible chains and new zero decomposition algorithm...In this paper, a Ritt-Wu＇s characteristic set method for ordinary difference systems is proposed, which is valid for any admissible ordering. New definition for irreducible chains and new zero decomposition algorithms are also proposed.展开更多
The two-dimensional magneto-hydrodynamic （MHD） equations are considered in this article. Viscous approximations are used to obtain the local existence and uniqueness of the classical solution. When the viscous term ...The two-dimensional magneto-hydrodynamic （MHD） equations are considered in this article. Viscous approximations are used to obtain the local existence and uniqueness of the classical solution. When the viscous term vanishes, the convergence rates, a main problem in turbulence, are also discussed. Moreover, a blow-up criterion for our classical solution is established in terms of the magnetic fields.展开更多
We obtained the Cα continuity for weak solutions of a class of ultraparabolic equations with measurable coeffcients of the form δt u = δx（a（x, y, t）δx u） ＋ b0（x, y, t）δxu ＋ b（x, y, t）δyu, which general...We obtained the Cα continuity for weak solutions of a class of ultraparabolic equations with measurable coeffcients of the form δt u = δx（a（x, y, t）δx u） ＋ b0（x, y, t）δxu ＋ b（x, y, t）δyu, which generalized our recent results on KFP equations.展开更多
In this paper we survey the authors＇ and related work on two-dimensional Riemann problems for hyperbolic conservation laws, mainly those related to the compressible Euler equations in gas dynamics. It contains four s...In this paper we survey the authors＇ and related work on two-dimensional Riemann problems for hyperbolic conservation laws, mainly those related to the compressible Euler equations in gas dynamics. It contains four sections： 1. Historical review. 2. Scalar conservation laws. 3. Euler equations. 4. Simplified models.展开更多
The multi-dimensional quantum hydrodynamic equations for charge transport in ultra-small electronic devices like semiconductors, where quantum effects （like particle tunnelling through potential barriers and built-up...The multi-dimensional quantum hydrodynamic equations for charge transport in ultra-small electronic devices like semiconductors, where quantum effects （like particle tunnelling through potential barriers and built-up in quantum wells） take place, is considered in the present paper, and the recent progress on well-posedness, stability analysis, and small scaling limits are reviewed.展开更多
In this paper, we study chaos control of the new 3D chaotic system. We use three feedback methods （the linear, speed, doubly-periodic function controller） to suppress the chaos to unstable equilibrium. As a result, ...In this paper, we study chaos control of the new 3D chaotic system. We use three feedback methods （the linear, speed, doubly-periodic function controller） to suppress the chaos to unstable equilibrium. As a result, some controllers are obtained. Moreover, numerical simulations are used to verify the effectiveness of the obtained controllers.展开更多
Based on computerized symbolic computation,a new method and its algorithm are proposed for searching for exact travelling wave solutions of the nonlinear partial differential equations.Making use of our approach,we in...Based on computerized symbolic computation,a new method and its algorithm are proposed for searching for exact travelling wave solutions of the nonlinear partial differential equations.Making use of our approach,we investigate the Whitham-Broer-Kaup equation in shallow water and obtain new families of exact solutions,which include soliton-like solutions and periodic solutions.As its special cases,the solutions of classical long wave equations and modified Boussinesq equations can also be found.展开更多
In this article, we investigate the global stability of the wave patterns with the superposition of viscous contact wave and rarefaction wave for the one-dimensional compressible Navier-Stokes equations with a free bo...In this article, we investigate the global stability of the wave patterns with the superposition of viscous contact wave and rarefaction wave for the one-dimensional compressible Navier-Stokes equations with a free boundary. It is shown that for the ideal polytropic gas, the superposition of the viscous contact wave with rarefaction wave is nonlinearly stable for the free boundary problem under the large initial perturbations for any γ 〉 1 with V being the adiabatic exponent provided that the wave strength is suitably small.展开更多
We study the following elliptic problem：{-div（a（x）Du）=Q（x）｜u｜2-2u＋λu x∈Ω,u=0 onδΩ Under certain assumptions on a and Q, we obtain existence of infinitely many solutions by variational method.
In this paper, we consider a class of reaction hyperbolic systems for axonal trans- port arising in neuroscience which can be regarded as hyperbolic systems with relaxation. We prove the BV entropy solutions of the hy...In this paper, we consider a class of reaction hyperbolic systems for axonal trans- port arising in neuroscience which can be regarded as hyperbolic systems with relaxation. We prove the BV entropy solutions of the hyperbolic systems converge toward to the unique entropy solution of the equilibrium equation at the optimal rate O（√δ） in L1 norm as the relaxation time δ tends to zero.展开更多
Based on noncommutative differential calculus, we present a theory of prolongation structure for semidiscrete non/inear evolution equations. As an illustrative example, a semi-discrete model of the non/inear SchrSding...Based on noncommutative differential calculus, we present a theory of prolongation structure for semidiscrete non/inear evolution equations. As an illustrative example, a semi-discrete model of the non/inear SchrSdinger equation is discussed in terms of this theory and the corresponding Lax pairs are also given.展开更多
This paper is concerned with the inverse problem of scattering of time-harmonic acoustic waves by an inhomogeneous penetrable obstacle in a piecewise homogeneous medium. The well-posedness of the direct problem is fir...This paper is concerned with the inverse problem of scattering of time-harmonic acoustic waves by an inhomogeneous penetrable obstacle in a piecewise homogeneous medium. The well-posedness of the direct problem is first established by using the integral equation method. We then proceed to establish two tools that play important roles for the inverse problem： one is a mixed reciprocity relation and the other is a priori estimates of the solution on some part of the interfaces between the layered media. For the inverse problem, we prove in this paper that both the penetrable interfaces and the possible inside inhomogeneity can be uniquely determined from a knowledge of the far field pattern for incident plane waves.展开更多
In this paper, we investigate symmetries of the new （4＋1）-dimensional Fokas equation, including point symmetries and the potential symmetries. We firstly employ the algorithmic procedure of computing the point symm...In this paper, we investigate symmetries of the new （4＋1）-dimensional Fokas equation, including point symmetries and the potential symmetries. We firstly employ the algorithmic procedure of computing the point symmetries. And then we transform the Fokas equation into a potential system and gain the potential symmetries of Fokas equation. Finally, we use the obtained point symmetries wave solutions and other solutions of the Fokas equation. and some constructive methods to get some doubly periodic In particular, some solitary wave solutions are also given.展开更多
This paper calculates the China-U.S. trade balance from the national income perspective based on an input-output model that differentiates domestic and foreign-invested companies. The result shows that due to differen...This paper calculates the China-U.S. trade balance from the national income perspective based on an input-output model that differentiates domestic and foreign-invested companies. The result shows that due to different degrees of dependence of both countries on foreign production factors such as foreign capital for the manufacturing of export goods,only 87.7% of the domestic value-added created by China's exports to the U.S. in 2012 was China's national income, whereas 96.2% of value-added in U.S. exports to China was U.S.national income. In the comparison of total export volume and export value-added, the home country's national income created by exports can more realistically reflect a country's gains from trade. In 2012, China's trade surplus with the U.S. stood at 102.8 billion US dollars in national income terms, which is 61% and 22% smaller than the results in gross and value-added terms, respectively. The implication is that the traditional trade balance accounting method seriously exaggerates the China-U.S. trade imbalance.展开更多
In this paper, a series of two line-soliton solutions and double periodic solutions of Chaffee-Infante equation have been obtained by using a new transformation. Unlike the existing methods which are used to find mult...In this paper, a series of two line-soliton solutions and double periodic solutions of Chaffee-Infante equation have been obtained by using a new transformation. Unlike the existing methods which are used to find multiple soliton solutions of nonlinear partial differential equations, this approach is constructive and pure algebraic. The results found here are tested on computer and therefore their validity is ensured.展开更多
Through the Wronskian technique, a simple and direct proof is presented that the AKNS hierarchy in the bilinear form has generalized double Wronskian solutions. Moreover, by using a unified way, soliton solutions, rat...Through the Wronskian technique, a simple and direct proof is presented that the AKNS hierarchy in the bilinear form has generalized double Wronskian solutions. Moreover, by using a unified way, soliton solutions, rational solutions, Matveev solutions and complexitons in double Wronskian form for it are constructed.展开更多
基金Supported by National Natural Science Foundation of China under Grant No.60821002/F02
文摘We analytically give the financial rogue waves in the nonlinear option pricing model due to Ivancevic,which is nonlinear wave alternative of the Black-Scholes model.These rogue wave solutions may be used to describe thepossible physical mechanisms for rogue wave phenomenon in financial markets and related fields.
文摘In this paper, a Ritt-Wu＇s characteristic set method for ordinary difference systems is proposed, which is valid for any admissible ordering. New definition for irreducible chains and new zero decomposition algorithms are also proposed.
基金The research is partially supported by NSF of China (10431060)NSF of Beijing (1042003)key project of NSFB-FBEC
文摘The two-dimensional magneto-hydrodynamic （MHD） equations are considered in this article. Viscous approximations are used to obtain the local existence and uniqueness of the classical solution. When the viscous term vanishes, the convergence rates, a main problem in turbulence, are also discussed. Moreover, a blow-up criterion for our classical solution is established in terms of the magnetic fields.
基金partially supported by the NSF of China (10325104)
文摘We obtained the Cα continuity for weak solutions of a class of ultraparabolic equations with measurable coeffcients of the form δt u = δx（a（x, y, t）δx u） ＋ b0（x, y, t）δxu ＋ b（x, y, t）δyu, which generalized our recent results on KFP equations.
基金supported by 973 Key program and the Key Program from Beijing Educational Commission with No. KZ200910028002Program for New Century Excellent Talents in University (NCET)+4 种基金Funding Project for Academic Human Resources Development in Institutions of Higher Learning Under the Jurisdiction of Beijing Municipality (PHR-IHLB)The research of Sheng partially supported by NSFC (10671120)Shanghai Leading Academic Discipline Project: J50101The research of Zhang partially supported by NSFC (10671120)The research of Zheng partially supported by NSF-DMS-0603859
文摘In this paper we survey the authors＇ and related work on two-dimensional Riemann problems for hyperbolic conservation laws, mainly those related to the compressible Euler equations in gas dynamics. It contains four sections： 1. Historical review. 2. Scalar conservation laws. 3. Euler equations. 4. Simplified models.
基金L.H. is supported in part by the NSFC (10431060) H.L. is supported partially by the NSFC (10431060, 10871134)+1 种基金the Beijing Nova program (2005B48)the NCET support of the Ministry of Education of China, and the Huo Ying Dong Foundation (111033)
文摘The multi-dimensional quantum hydrodynamic equations for charge transport in ultra-small electronic devices like semiconductors, where quantum effects （like particle tunnelling through potential barriers and built-up in quantum wells） take place, is considered in the present paper, and the recent progress on well-posedness, stability analysis, and small scaling limits are reviewed.
基金The project supported by Natural Science Foundations of Zhejiang Province of China under Grant No.Y604056the Doctoral Foundation of Ningbo City under Grant No.2005A61030+1 种基金National Natural Science Foundation of China under Grant No.10401039National Key Basic Research Program of China under Grant No.2004CB318000,and the NDEF,CAS
文摘In this paper, we study chaos control of the new 3D chaotic system. We use three feedback methods （the linear, speed, doubly-periodic function controller） to suppress the chaos to unstable equilibrium. As a result, some controllers are obtained. Moreover, numerical simulations are used to verify the effectiveness of the obtained controllers.
文摘Based on computerized symbolic computation,a new method and its algorithm are proposed for searching for exact travelling wave solutions of the nonlinear partial differential equations.Making use of our approach,we investigate the Whitham-Broer-Kaup equation in shallow water and obtain new families of exact solutions,which include soliton-like solutions and periodic solutions.As its special cases,the solutions of classical long wave equations and modified Boussinesq equations can also be found.
基金supported by NSFC Grant No.11171153supported by NSFC Grant No.11322106supported by the Fundamental Research Funds for the Central Universities No.2015ZCQ-LY-01 and No.BLX2015-27
文摘In this article, we investigate the global stability of the wave patterns with the superposition of viscous contact wave and rarefaction wave for the one-dimensional compressible Navier-Stokes equations with a free boundary. It is shown that for the ideal polytropic gas, the superposition of the viscous contact wave with rarefaction wave is nonlinearly stable for the free boundary problem under the large initial perturbations for any γ 〉 1 with V being the adiabatic exponent provided that the wave strength is suitably small.
基金supported by Key Project (10631030) of NSFCKnowledge Innovation Funds of CAS in Chinasupported by ARC in Australia
文摘We study the following elliptic problem：{-div（a（x）Du）=Q（x）｜u｜2-2u＋λu x∈Ω,u=0 onδΩ Under certain assumptions on a and Q, we obtain existence of infinitely many solutions by variational method.
基金partially supported by the NSFC(11371349)National Basic Research Program of China(973 Program)(2011CB808002)
文摘In this paper, we consider a class of reaction hyperbolic systems for axonal trans- port arising in neuroscience which can be regarded as hyperbolic systems with relaxation. We prove the BV entropy solutions of the hyperbolic systems converge toward to the unique entropy solution of the equilibrium equation at the optimal rate O（√δ） in L1 norm as the relaxation time δ tends to zero.
基金The project supported by Tianyuan Foundation for Mathematics under Grant No. 10626016 of National Natural Science Foundation of China, China Postdoctoral Science Foundation, Beijing Jiao-Wei Key Project under Grant No. KZ 200310028010, and National Natural Science Foundation of China under Grant No. 10375038
文摘Based on noncommutative differential calculus, we present a theory of prolongation structure for semidiscrete non/inear evolution equations. As an illustrative example, a semi-discrete model of the non/inear SchrSdinger equation is discussed in terms of this theory and the corresponding Lax pairs are also given.
基金the first author (XL) was supported by the China Postdoctoral Science Foundation (20100480494)the NSF of China (11101412)+1 种基金K.C. Wong Education Foundation, Hong Kongthe second author (BZ) was supported by the NSF of China (11071244,11161130002)
文摘This paper is concerned with the inverse problem of scattering of time-harmonic acoustic waves by an inhomogeneous penetrable obstacle in a piecewise homogeneous medium. The well-posedness of the direct problem is first established by using the integral equation method. We then proceed to establish two tools that play important roles for the inverse problem： one is a mixed reciprocity relation and the other is a priori estimates of the solution on some part of the interfaces between the layered media. For the inverse problem, we prove in this paper that both the penetrable interfaces and the possible inside inhomogeneity can be uniquely determined from a knowledge of the far field pattern for incident plane waves.
基金supported by the National Natural Science Foundation of China under Grant No.60821002the National Key Basic Research Program of China under Grant No.2004CB318000
文摘In this paper, we investigate symmetries of the new （4＋1）-dimensional Fokas equation, including point symmetries and the potential symmetries. We firstly employ the algorithmic procedure of computing the point symmetries. And then we transform the Fokas equation into a potential system and gain the potential symmetries of Fokas equation. Finally, we use the obtained point symmetries wave solutions and other solutions of the Fokas equation. and some constructive methods to get some doubly periodic In particular, some solitary wave solutions are also given.
基金supported by the National Natural Science Foundation of China (NSFC) projects (71473244, 61873261 and 71704195)the Fundamental Research Funds for the Central Universities,the University of International Business and Economics (CXTD7-06)
文摘This paper calculates the China-U.S. trade balance from the national income perspective based on an input-output model that differentiates domestic and foreign-invested companies. The result shows that due to different degrees of dependence of both countries on foreign production factors such as foreign capital for the manufacturing of export goods,only 87.7% of the domestic value-added created by China's exports to the U.S. in 2012 was China's national income, whereas 96.2% of value-added in U.S. exports to China was U.S.national income. In the comparison of total export volume and export value-added, the home country's national income created by exports can more realistically reflect a country's gains from trade. In 2012, China's trade surplus with the U.S. stood at 102.8 billion US dollars in national income terms, which is 61% and 22% smaller than the results in gross and value-added terms, respectively. The implication is that the traditional trade balance accounting method seriously exaggerates the China-U.S. trade imbalance.
基金The project supported by '973' Project under Grant No.2004CB318000Doctor Start-up Foundation of Liaoning Province under Grant No.1040225Science and Technology Research Project of Liaoning Education Bureau
文摘In this paper, a series of two line-soliton solutions and double periodic solutions of Chaffee-Infante equation have been obtained by using a new transformation. Unlike the existing methods which are used to find multiple soliton solutions of nonlinear partial differential equations, this approach is constructive and pure algebraic. The results found here are tested on computer and therefore their validity is ensured.
基金National Natural Science Foundation of China under Grant No.10371070the Special Found for Major Specialities of Shanghai Education CommitteeChina Postdoctoral Science Foundation
文摘Through the Wronskian technique, a simple and direct proof is presented that the AKNS hierarchy in the bilinear form has generalized double Wronskian solutions. Moreover, by using a unified way, soliton solutions, rational solutions, Matveev solutions and complexitons in double Wronskian form for it are constructed.
