Starting from an extended mapping approach, a new type of variable separation solution with arbitrary functions of generalized (2+1)-dimensional Broer-Kaup system (GBK) system is derived. Then based on the derived sol...Starting from an extended mapping approach, a new type of variable separation solution with arbitrary functions of generalized (2+1)-dimensional Broer-Kaup system (GBK) system is derived. Then based on the derived solitary wave solution, we obtain some specific chaotic solitons to the (2+1)-dimensional GBK system.展开更多
In this paper, we extend the mapping approach to the N-order Schrodinger equation. In terms of the extended mapping approach, new families of variable separation solutions with some arbitrary functions are derived.
Starting from a special variable transformation and with the help of an extended mapping approach, the high-order Schrodinger equation （n = 3, 4） is solved. A new family of variable separation solutions with arbitra...Starting from a special variable transformation and with the help of an extended mapping approach, the high-order Schrodinger equation （n = 3, 4） is solved. A new family of variable separation solutions with arbitrary functions is derived.展开更多
In this paper,we extend the mapping transformation method through introducing variable coefficients.By means of the extended mapping transformation method,many explicit and exact general solutions with arbitrary funct...In this paper,we extend the mapping transformation method through introducing variable coefficients.By means of the extended mapping transformation method,many explicit and exact general solutions with arbitrary functions for some nonlinear partial differential equations,which contain solitary wave solutions,trigonometric function solutions,and rational solutions,are obtained.展开更多
Extended mapping approach is introduced to solve （2＋1）-dimensional Nizhnik-Novikov Veselov equation. A new type of variable separation solutions is derived with arbitrary functions in the model. Based on this excit...Extended mapping approach is introduced to solve （2＋1）-dimensional Nizhnik-Novikov Veselov equation. A new type of variable separation solutions is derived with arbitrary functions in the model. Based on this excitation, rich localized structures such as multi-lump soliton and ring soliton are revealed by selecting the arbitrary function appropriately.展开更多
Three-party password-based key agreement protocols allow two users to authenticate each other via a public channel and establish a session key with the aid of a trusted server. Recently, Farash et al. [Farash M S, Att...Three-party password-based key agreement protocols allow two users to authenticate each other via a public channel and establish a session key with the aid of a trusted server. Recently, Farash et al. [Farash M S, Attari M A 2014 ＂An efficient and provably secure three-party password-based authenticated key exchange protocol based on Chebyshev chaotic maps＂, Nonlinear Dynamics 77（7）： 399-411] proposed a three-party key agreement protocol by using the extended chaotic maps. They claimed that their protocol could achieve strong security. In the present paper, we analyze Farash et al.＇s protocol and point out that this protocol is vulnerable to off-line password guessing attack and suffers communication burden. To handle the issue, we propose an efficient three-party password-based key agreement protocol using extended chaotic maps, which uses neither symmetric cryptosystems nor the server＇s public key. Compared with the relevant schemes, our protocol provides better performance in terms of computation and communication. Therefore, it is suitable for practical applications.展开更多
With the help of an extended mapping approach, a new type of variable separation excitation with three arbitrary functions of the (2+1)-dimensional dispersive long-water wave system (DLW) is derived. Based on the deri...With the help of an extended mapping approach, a new type of variable separation excitation with three arbitrary functions of the (2+1)-dimensional dispersive long-water wave system (DLW) is derived. Based on the derived variable separation excitation, abundant non-propagating solitons such as dromion, ring, peakon, and compacton etc.are revealed by selecting appropriate functions in this paper.展开更多
By making use of extended mapping method and auxiliary equation for finding new periodic wave solu tions of nonlinear evolution equations in mathematical physics, we obtain some new periodic wave solutions for general...By making use of extended mapping method and auxiliary equation for finding new periodic wave solu tions of nonlinear evolution equations in mathematical physics, we obtain some new periodic wave solutions for generalized Klein-Cordon equation and Benjamin equation, which cannot be found in previous work. This method also can be used to find new periodic wave solutions of other nonlinear evolution equations.展开更多
The searching exact solutions in the solitary wave form of non-linear partial differential equations （PDEs） play a significant role to understand the internal mechanism of complex physical phenomena. In this paper w...The searching exact solutions in the solitary wave form of non-linear partial differential equations （PDEs） play a significant role to understand the internal mechanism of complex physical phenomena. In this paper we employ the proposed modified extended mapping method for constructing the exact solitary wave and soliton solutions of coupled Klein-Gordon equations and the （2-1-1）-dimensional cubic Klein-Gordon （K-G） equation. The Klein-Gordon equations are relativistic version of Schr6dinger equations, which describe the relation of relativistic energy-momentum in the form of quantized version. We productively achieve exact solutions involving parameters such as dark and bright solitary waves, Kink solitary wave, anti-Kink solitary wave, periodic solitary waves, and hyperbolic functions in which several solutions are novel. We plot the three-dimensional surface of some obtained solutions in this study. It is recognized that the modified mapping technique presents a more prestigious mathematical tool for acquiring analytical solutions of PDEs arise in mathematical physics.展开更多
Applying the extended mapping method via Riccati equation, many exact variable separation solutions for the （2＆1 ）-dimensional variable coefficient Broer-Kaup equation are obtained. Introducing multiple valued func...Applying the extended mapping method via Riccati equation, many exact variable separation solutions for the （2＆1 ）-dimensional variable coefficient Broer-Kaup equation are obtained. Introducing multiple valued function and Jacobi elliptic function in the seed solution, special types of periodic semifolded solitary waves are derived. In the long wave limit these periodic semifolded solitary wave excitations may degenerate into single semifolded localized soliton structures. The interactions of the periodic semifolded solitary waves and their degenerated single semifolded soliton structures are investigated graphically and found to be completely elastic.展开更多
Abundant new exact solutions of the Schamel-Korteweg-de Vries （S-KdV） equation and modified Zakharov- Kuznetsov equation arising in plasma and dust plasma are presented by using the extended mapping method and the a...Abundant new exact solutions of the Schamel-Korteweg-de Vries （S-KdV） equation and modified Zakharov- Kuznetsov equation arising in plasma and dust plasma are presented by using the extended mapping method and the availability of symbolic computation. These solutions include the Jacobi elliptic function solutions, hyperbolic function solutions, rational solutions, and periodic wave solutions. In the limiting cases, the solitary wave solutions are obtained and some known solutions are also recovered.展开更多
Starting from the extended mapping approach and a linear variable separation method, we find new families of variable separation solutions with some arbitrary functions for the （3＋1）-dimensionM Burgers system. Then...Starting from the extended mapping approach and a linear variable separation method, we find new families of variable separation solutions with some arbitrary functions for the （3＋1）-dimensionM Burgers system. Then based on the derived exact solutions, some novel and interesting localized coherent excitations such as embedded-solitons, taper-like soliton, complex wave excitations in the periodic wave background are revealed by introducing appropriate boundary conditions and/or initial qualifications. The evolutional properties of the complex wave excitations are briefly investigated.展开更多
By means of an extended mapping approach and a linear variable separation approach,a new family ofexact solutions of the general(2+1)-dimensional Korteweg de Vries system(GKdV)are derived.Based on the derivedsolitary ...By means of an extended mapping approach and a linear variable separation approach,a new family ofexact solutions of the general(2+1)-dimensional Korteweg de Vries system(GKdV)are derived.Based on the derivedsolitary wave excitation,we obtain some special peakon excitations and fractal dromions in this short note.展开更多
With an extended mapping approach and a linear variable separation method, new families of variable separation solutions （including solitary wave solutions, periodic wave solutions, and rational function solutions） ...With an extended mapping approach and a linear variable separation method, new families of variable separation solutions （including solitary wave solutions, periodic wave solutions, and rational function solutions） with arbitrary functions for （3＋1）-dimensionai Burgers system is derived. Based on the derived excitations, we obtain some novel localized coherent structures and study the interactions between solitons.展开更多
With the help of an extended mapping approach and a linear variable separation method,new families ofvariable separation solutions with arbitrary functions for the(3+1)-dimensional Burgers system are derived.Based ont...With the help of an extended mapping approach and a linear variable separation method,new families ofvariable separation solutions with arbitrary functions for the(3+1)-dimensional Burgers system are derived.Based onthe derived exact solutions,some novel and interesting localized coherent excitations such as embed-solitons are revealedby selecting appropriate boundary conditions and/or initial qualifications.The time evolutional properties of the novellocalized excitation are also briefly investigated.展开更多
A non-traveling wave solution of a generalized Vakhnenko equation arising from the high-frequent wave motion in a relaxing medium is derived via the extended Riccati mapping method.The solution includes an arbitrary f...A non-traveling wave solution of a generalized Vakhnenko equation arising from the high-frequent wave motion in a relaxing medium is derived via the extended Riccati mapping method.The solution includes an arbitrary function of an independent variable.Based on the solution,two hyperbolic functions are chosen to construct new solitons.Novel single-loop-like and double-loop-like solitons are found for the equation.展开更多
基金浙江省自然科学基金，Foundation of New Century "151 Talent Engineering" of Zhejiang Province，丽水学院校科研和教改项目，the Scientific Research Foundation of Key Discipline of Zhejiang Province
文摘Starting from an extended mapping approach, a new type of variable separation solution with arbitrary functions of generalized (2+1)-dimensional Broer-Kaup system (GBK) system is derived. Then based on the derived solitary wave solution, we obtain some specific chaotic solitons to the (2+1)-dimensional GBK system.
基金The project supported by the Natural Science Foundation of Zhejiang Province of China under Grant No. Y604106, the Foundation of New Century ＂151 Talent Engineering＂ of Zhejiang Province, the Scientific Research Foundation of Key Discipline of Zhejiang Province, and the Natural Science Foundation of Zhejiang Lishui University under Grant No. KZ05005
文摘In this paper, we extend the mapping approach to the N-order Schrodinger equation. In terms of the extended mapping approach, new families of variable separation solutions with some arbitrary functions are derived.
基金The project supported by the Natural Science Foundation of Zhejiang Province of China under Grant No. Y604106, the Foundation of New Century ＂151 Talent Engineering＂ of Zhejiang Province, the Scientific Research Foundation of Key Discipline of Zhejiang Province, and the Natural Science Foundation of Zhejiang Lishui University under Grant No. KZ04008
文摘Starting from a special variable transformation and with the help of an extended mapping approach, the high-order Schrodinger equation （n = 3, 4） is solved. A new family of variable separation solutions with arbitrary functions is derived.
基金by National Natural Science Foundation of China and the Natural Sclence Foundation of Shandong Province of China
文摘In this paper,we extend the mapping transformation method through introducing variable coefficients.By means of the extended mapping transformation method,many explicit and exact general solutions with arbitrary functions for some nonlinear partial differential equations,which contain solitary wave solutions,trigonometric function solutions,and rational solutions,are obtained.
基金The authors would like to thank Profs. Jie-Fang Zhang and Chun-Long Zheng for helpful discussions.
文摘Extended mapping approach is introduced to solve （2＋1）-dimensional Nizhnik-Novikov Veselov equation. A new type of variable separation solutions is derived with arbitrary functions in the model. Based on this excitation, rich localized structures such as multi-lump soliton and ring soliton are revealed by selecting the arbitrary function appropriately.
基金Project supported by the National Natural Science Foundation of China(Grant No.61462033)
文摘Three-party password-based key agreement protocols allow two users to authenticate each other via a public channel and establish a session key with the aid of a trusted server. Recently, Farash et al. [Farash M S, Attari M A 2014 ＂An efficient and provably secure three-party password-based authenticated key exchange protocol based on Chebyshev chaotic maps＂, Nonlinear Dynamics 77（7）： 399-411] proposed a three-party key agreement protocol by using the extended chaotic maps. They claimed that their protocol could achieve strong security. In the present paper, we analyze Farash et al.＇s protocol and point out that this protocol is vulnerable to off-line password guessing attack and suffers communication burden. To handle the issue, we propose an efficient three-party password-based key agreement protocol using extended chaotic maps, which uses neither symmetric cryptosystems nor the server＇s public key. Compared with the relevant schemes, our protocol provides better performance in terms of computation and communication. Therefore, it is suitable for practical applications.
文摘With the help of an extended mapping approach, a new type of variable separation excitation with three arbitrary functions of the (2+1)-dimensional dispersive long-water wave system (DLW) is derived. Based on the derived variable separation excitation, abundant non-propagating solitons such as dromion, ring, peakon, and compacton etc.are revealed by selecting appropriate functions in this paper.
基金The project supported by the Natural Science Foundation of Anhui Province of China under Grant No. 01041188 and the Foundation of Classical Courses of Anhui Province
文摘By making use of extended mapping method and auxiliary equation for finding new periodic wave solu tions of nonlinear evolution equations in mathematical physics, we obtain some new periodic wave solutions for generalized Klein-Cordon equation and Benjamin equation, which cannot be found in previous work. This method also can be used to find new periodic wave solutions of other nonlinear evolution equations.
文摘The searching exact solutions in the solitary wave form of non-linear partial differential equations （PDEs） play a significant role to understand the internal mechanism of complex physical phenomena. In this paper we employ the proposed modified extended mapping method for constructing the exact solitary wave and soliton solutions of coupled Klein-Gordon equations and the （2-1-1）-dimensional cubic Klein-Gordon （K-G） equation. The Klein-Gordon equations are relativistic version of Schr6dinger equations, which describe the relation of relativistic energy-momentum in the form of quantized version. We productively achieve exact solutions involving parameters such as dark and bright solitary waves, Kink solitary wave, anti-Kink solitary wave, periodic solitary waves, and hyperbolic functions in which several solutions are novel. We plot the three-dimensional surface of some obtained solutions in this study. It is recognized that the modified mapping technique presents a more prestigious mathematical tool for acquiring analytical solutions of PDEs arise in mathematical physics.
基金National Natural Science Foundation of China under Grant Nos.10472063 and 10672096
文摘Applying the extended mapping method via Riccati equation, many exact variable separation solutions for the （2＆1 ）-dimensional variable coefficient Broer-Kaup equation are obtained. Introducing multiple valued function and Jacobi elliptic function in the seed solution, special types of periodic semifolded solitary waves are derived. In the long wave limit these periodic semifolded solitary wave excitations may degenerate into single semifolded localized soliton structures. The interactions of the periodic semifolded solitary waves and their degenerated single semifolded soliton structures are investigated graphically and found to be completely elastic.
文摘Abundant new exact solutions of the Schamel-Korteweg-de Vries （S-KdV） equation and modified Zakharov- Kuznetsov equation arising in plasma and dust plasma are presented by using the extended mapping method and the availability of symbolic computation. These solutions include the Jacobi elliptic function solutions, hyperbolic function solutions, rational solutions, and periodic wave solutions. In the limiting cases, the solitary wave solutions are obtained and some known solutions are also recovered.
基金the Natural Science Foundation of Zhejiang Province under Grant Nos.Y604106 and Y606181the Foundation of New Century"151 Talent Engineering"of Zhejiang Provincethe Scientific Research Foundation of Key Discipline of Zhejiang Province
文摘Starting from the extended mapping approach and a linear variable separation method, we find new families of variable separation solutions with some arbitrary functions for the （3＋1）-dimensionM Burgers system. Then based on the derived exact solutions, some novel and interesting localized coherent excitations such as embedded-solitons, taper-like soliton, complex wave excitations in the periodic wave background are revealed by introducing appropriate boundary conditions and/or initial qualifications. The evolutional properties of the complex wave excitations are briefly investigated.
基金The project supported by the Natural Science Foundation of Zhejiang Province under Grant No.Y604106the Natural Science Foundation of Zhejiang Lishui University under Grant No.KZ05010
文摘By means of an extended mapping approach and a linear variable separation approach,a new family ofexact solutions of the general(2+1)-dimensional Korteweg de Vries system(GKdV)are derived.Based on the derivedsolitary wave excitation,we obtain some special peakon excitations and fractal dromions in this short note.
基金The project supported by the Natural Science Foundation of Zhejiang Province under Grant Nos.Y606128 and Y604106the Natural Science Foundation of Zhejiang Lishui University under Grant Nos.FC06001 and QN06009
文摘With an extended mapping approach and a linear variable separation method, new families of variable separation solutions （including solitary wave solutions, periodic wave solutions, and rational function solutions） with arbitrary functions for （3＋1）-dimensionai Burgers system is derived. Based on the derived excitations, we obtain some novel localized coherent structures and study the interactions between solitons.
基金the Natural Science Foundation of Zhejiang Province under Grant Nos.Y604106 and Y606181the Foundation of New Century"151 Talent Engineering"of Zhejiang Province+1 种基金the Scientific Research Foundation of Key Discipline of Zhejiang Provincethe Natural Science Foundation of Zhejiang Lishui University under Grant No KZ06006
文摘With the help of an extended mapping approach and a linear variable separation method,new families ofvariable separation solutions with arbitrary functions for the(3+1)-dimensional Burgers system are derived.Based onthe derived exact solutions,some novel and interesting localized coherent excitations such as embed-solitons are revealedby selecting appropriate boundary conditions and/or initial qualifications.The time evolutional properties of the novellocalized excitation are also briefly investigated.
基金Project supported by the Scientific Research Common Program of Beijing Municipal Commission of Education,China (Grant No. KM201010011001),PHR(Grant No. 201106206)the Funding Project for Innovation on Science,Technology and Graduate Education in Institutions of Higher Learning Under the Jurisdiction of Beijing Municipality,China (Grant Nos. 201098,PXM2012 014213 000087,PXM2012 014213 000037,and PXM2012 014213 000079)
文摘A non-traveling wave solution of a generalized Vakhnenko equation arising from the high-frequent wave motion in a relaxing medium is derived via the extended Riccati mapping method.The solution includes an arbitrary function of an independent variable.Based on the solution,two hyperbolic functions are chosen to construct new solitons.Novel single-loop-like and double-loop-like solitons are found for the equation.
