Exact periodic-wave solutions to the generalized Nizhnik-Novikov-Veselov (NNV) equation are obtained by using the extended Jacobi elliptic-function method, and in the limit case, the solitary wave solution to NNV equa...Exact periodic-wave solutions to the generalized Nizhnik-Novikov-Veselov (NNV) equation are obtained by using the extended Jacobi elliptic-function method, and in the limit case, the solitary wave solution to NNV equation are also obtained.展开更多
Methods and techniques for the identification, monitoring and management of natural hazards in high mountain areas are enumerated and described. A case study from the western Himalayan Kullu District in Himachal Prade...Methods and techniques for the identification, monitoring and management of natural hazards in high mountain areas are enumerated and described. A case study from the western Himalayan Kullu District in Himachal Pradesh, India is used to illustrate some of the methods. Research on the general topic has been conducted over three decades and that in the Kullu District has been carried out since 1994. Early methods of hazards identification in high mountain areas involved intensive and lengthy fieldwork and mapping with primary reliance on interpretation of landforms, sediments and vegetation thought to be indicative of slope failures, rock falls, debris flows, floods and accelerated soil surface erosion. Augmented by the use of airphotos and ad hoc observations of specific events over time, these methods resulted in the gradual accumulation of information on hazardous sites and the beginnings of a chronology of occurrences in an area. The use of historical methods applied to written and photographic material, often held in archives and libraries, further improved the resolution of hazards information. In the past two decades, both the need for, and the ability to, accurately identify potential hazards have increased. The need for accurate information and monitoring comes about as a result of rapid growth in population, settlements, transportation infrastructure and intensified land uses and, therefore, risk and vulnerability in mountain areas. Ability has improved as the traditional methods of gathering and manipulating data have been supplemented by the use of remote sensing, automated terrain modeling, global positioning systems and geographical information systems. This paper focuses on the development and application of the latter methods and techniques to characterize and monitor hazards in high mountain areas.展开更多
In this paper, two transformations are introduced to solve sinh-Gordon equation by using the knowledge of elliptic equation and Jacobian elliptic functions. It is shown that different transformations are required in o...In this paper, two transformations are introduced to solve sinh-Gordon equation by using the knowledge of elliptic equation and Jacobian elliptic functions. It is shown that different transformations are required in order to obtain more kinds of solutions to the sinh-Gordon equation.展开更多
One of the advantages of the variational iteration method is the free choice of initial guess. In this paper we use the basic idea of the Jacobian-function method to construct a generalized trial function with some un...One of the advantages of the variational iteration method is the free choice of initial guess. In this paper we use the basic idea of the Jacobian-function method to construct a generalized trial function with some unknown parameters. The Jaulent-Miodek equations are used to illustrate effectiveness and convenience of this method, some new explicit exact travelling wave solutions have been obtained, which include bell-type soliton solution, kink-type soliton solutions, solitary wave solutions, and doubly periodic wave solutions.展开更多
Subalpine forests are known as outstanding habitats due to co-existence of both temperate and alpine vegetation and are classic example of ecotonal zones. Limited but diverse physiognomy of trees inhabiting in subalpi...Subalpine forests are known as outstanding habitats due to co-existence of both temperate and alpine vegetation and are classic example of ecotonal zones. Limited but diverse physiognomy of trees inhabiting in subalpine forest results in variability within under-canopy habitat conditions. Studies were undertaken to assess population status, habitat preference and interferences to the trees and associated under-canopy herbs in a subalpine forest of western Himalaya. A total of lo woody and 23 under-canopy herbs were recorded in the selected subalpine forest area. At each stand, the number of tree species and under-canopy herbs ranged from 2 to 4 and 8 to lo respectively. Abies spectabilis, Acer caesium, Quercus floribunda, Q. semecarpifolia and Rhododendron arboreum were key tree species in this area. The density of main woody species was 280 to 119o individuals ha-1 at different stands. Herbaceous plants with rosette and clump growth habits were observed to have higher values for total basal cover and importance value index. Presence of some under- canopy herbs like; Dactylorhiza hatagirea, Malaxis muscifera, Picrorhiza kurrooa, Polygonatum cirrhifolium habitats also and Skimmia laureola showed that they are in the habitat specific specific. However, the presence of Frageria nubicola and Viola sp. was common in the selected stands. Felling of trees for timber, construction of temporary huts, fuel wood and lopping for fodder were main interferences for trees. On the other hand, trampling driven damage due to grazing, habitats degradation and overexploitation were observed key threats for under-canopy herbs. Integrated analysis including population studies, habitats preference and interferences to the trees and under-canopy herbs in this sensitive and important ecosystem will be useful for determining the conservation plans and ecosystem management.展开更多
By means of the standard truncated Painlevé expansion and a variable separation approach, a general variable separation solution of the generalized Burgers system is derived. In addition to the usual localized co...By means of the standard truncated Painlevé expansion and a variable separation approach, a general variable separation solution of the generalized Burgers system is derived. In addition to the usual localized coherent soliton excitations like dromions, lumps, rings, breathers, instantons, oscillating soliton excitations, peakons, foldons, and previously revealed chaotic and fractal localized solutions, some new types of excitations — compacton and Jacobi periodic wave solutions are obtained by introducing appropriate lower dimensional piecewise smooth functions and Jacobi elliptic functions.展开更多
In this paper, new basic functions, which are composed of three basic Jacobi elliptic functions, are chosen as components of finite expansion. This finite expansion can be taken as an ansatz and applied to solve nonli...In this paper, new basic functions, which are composed of three basic Jacobi elliptic functions, are chosen as components of finite expansion. This finite expansion can be taken as an ansatz and applied to solve nonlinear wave equations. As an example, mKdV equation is solved, and more new rational form solutions are derived, such as periodic solutions of rational form, solitary wave solutions of rational form, and so on.展开更多
The Jacobi elliptic function expansion method is extended to derive the explicit periodic wave solutions for nonlinear differential-difference equations. Three well-known examples are chosen to illustrate the applicat...The Jacobi elliptic function expansion method is extended to derive the explicit periodic wave solutions for nonlinear differential-difference equations. Three well-known examples are chosen to illustrate the application of the Jacobi elliptic function expansion method. As a result, three types of periodic wave solutions including Jacobi elliptic sine function, Jacobi elliptic cosine function and the third elliptic function solutions are obtained. It is shown that the shock wave solutions and solitary wave solutions can be obtained at their limit condition.展开更多
The elliptic equation is taken as a transformation and applied to solve nonlinear wave equations. It is shown that this method is more powerful to give more kinds of solutions, such as rational solutions, solitary wav...The elliptic equation is taken as a transformation and applied to solve nonlinear wave equations. It is shown that this method is more powerful to give more kinds of solutions, such as rational solutions, solitary wave solutions,periodic wave solutions and so on, so it can be taken as a generalized method.展开更多
Based on the multi-linear variable separation approach, a class of exact, doubly periodic wave solutions for the （3＋1）-dimensional Jimbo-Miwa equation is analytically obtained by choosing the Jacobi elliptic functi...Based on the multi-linear variable separation approach, a class of exact, doubly periodic wave solutions for the （3＋1）-dimensional Jimbo-Miwa equation is analytically obtained by choosing the Jacobi elliptic functions and their combinations. Limit cases are considered and some new solitary structures （new dromions） are derived. The interaction properties of periodic waves are numerically studied and found to be inelastic. Under long wave limit, two sets of new solution structures （dromions） are given. The interaction properties of these solutions reveal that some of them are completely elastic and some are inelastic.展开更多
An extended hyperbola function method is proposed to construct exact solitary wave solutions to nonlinear wave equation based upon a coupled Riccati equation. It is shown that more new solitary wave solutions can be f...An extended hyperbola function method is proposed to construct exact solitary wave solutions to nonlinear wave equation based upon a coupled Riccati equation. It is shown that more new solitary wave solutions can be found by this new method, which include kink-shaped soliton solutions, bell-shaped soliton solutions and new solitary wave.The new method can be applied to other nonlinear equations in mathematical physics.展开更多
基金Yunnan Provincial Department of Education Science Research Fund Project(2018JS709)National Natural Science Foundation of China(81973264)Guangdong Basic and Applied Basic Research Foundation(2019A1515011954,2020A1515010593)。
文摘Exact periodic-wave solutions to the generalized Nizhnik-Novikov-Veselov (NNV) equation are obtained by using the extended Jacobi elliptic-function method, and in the limit case, the solitary wave solution to NNV equation are also obtained.
文摘Methods and techniques for the identification, monitoring and management of natural hazards in high mountain areas are enumerated and described. A case study from the western Himalayan Kullu District in Himachal Pradesh, India is used to illustrate some of the methods. Research on the general topic has been conducted over three decades and that in the Kullu District has been carried out since 1994. Early methods of hazards identification in high mountain areas involved intensive and lengthy fieldwork and mapping with primary reliance on interpretation of landforms, sediments and vegetation thought to be indicative of slope failures, rock falls, debris flows, floods and accelerated soil surface erosion. Augmented by the use of airphotos and ad hoc observations of specific events over time, these methods resulted in the gradual accumulation of information on hazardous sites and the beginnings of a chronology of occurrences in an area. The use of historical methods applied to written and photographic material, often held in archives and libraries, further improved the resolution of hazards information. In the past two decades, both the need for, and the ability to, accurately identify potential hazards have increased. The need for accurate information and monitoring comes about as a result of rapid growth in population, settlements, transportation infrastructure and intensified land uses and, therefore, risk and vulnerability in mountain areas. Ability has improved as the traditional methods of gathering and manipulating data have been supplemented by the use of remote sensing, automated terrain modeling, global positioning systems and geographical information systems. This paper focuses on the development and application of the latter methods and techniques to characterize and monitor hazards in high mountain areas.
基金The project supported by National Natural Science Foundation of China under Grant No. 40305006
文摘In this paper, two transformations are introduced to solve sinh-Gordon equation by using the knowledge of elliptic equation and Jacobian elliptic functions. It is shown that different transformations are required in order to obtain more kinds of solutions to the sinh-Gordon equation.
基金National Natural Science Foundation of China under Grant No.10172056
文摘One of the advantages of the variational iteration method is the free choice of initial guess. In this paper we use the basic idea of the Jacobian-function method to construct a generalized trial function with some unknown parameters. The Jaulent-Miodek equations are used to illustrate effectiveness and convenience of this method, some new explicit exact travelling wave solutions have been obtained, which include bell-type soliton solution, kink-type soliton solutions, solitary wave solutions, and doubly periodic wave solutions.
文摘Subalpine forests are known as outstanding habitats due to co-existence of both temperate and alpine vegetation and are classic example of ecotonal zones. Limited but diverse physiognomy of trees inhabiting in subalpine forest results in variability within under-canopy habitat conditions. Studies were undertaken to assess population status, habitat preference and interferences to the trees and associated under-canopy herbs in a subalpine forest of western Himalaya. A total of lo woody and 23 under-canopy herbs were recorded in the selected subalpine forest area. At each stand, the number of tree species and under-canopy herbs ranged from 2 to 4 and 8 to lo respectively. Abies spectabilis, Acer caesium, Quercus floribunda, Q. semecarpifolia and Rhododendron arboreum were key tree species in this area. The density of main woody species was 280 to 119o individuals ha-1 at different stands. Herbaceous plants with rosette and clump growth habits were observed to have higher values for total basal cover and importance value index. Presence of some under- canopy herbs like; Dactylorhiza hatagirea, Malaxis muscifera, Picrorhiza kurrooa, Polygonatum cirrhifolium habitats also and Skimmia laureola showed that they are in the habitat specific specific. However, the presence of Frageria nubicola and Viola sp. was common in the selected stands. Felling of trees for timber, construction of temporary huts, fuel wood and lopping for fodder were main interferences for trees. On the other hand, trampling driven damage due to grazing, habitats degradation and overexploitation were observed key threats for under-canopy herbs. Integrated analysis including population studies, habitats preference and interferences to the trees and under-canopy herbs in this sensitive and important ecosystem will be useful for determining the conservation plans and ecosystem management.
基金The project supported by National Natural Science Foundation of China under Grant No.10172056+2 种基金the Natural Science Foundation of Zhengjiang Provincethe Foundation of Zhengjiang Lishui College under Grant Nos.KZ03009 and KZ03005
文摘By means of the standard truncated Painlevé expansion and a variable separation approach, a general variable separation solution of the generalized Burgers system is derived. In addition to the usual localized coherent soliton excitations like dromions, lumps, rings, breathers, instantons, oscillating soliton excitations, peakons, foldons, and previously revealed chaotic and fractal localized solutions, some new types of excitations — compacton and Jacobi periodic wave solutions are obtained by introducing appropriate lower dimensional piecewise smooth functions and Jacobi elliptic functions.
基金The project supported by National Natural Science Foundation of China under Grant No.40305006the Ministry of Science and Technology of China through Special Public Welfare Project under Grant No.2002DIB20070
文摘In this paper, new basic functions, which are composed of three basic Jacobi elliptic functions, are chosen as components of finite expansion. This finite expansion can be taken as an ansatz and applied to solve nonlinear wave equations. As an example, mKdV equation is solved, and more new rational form solutions are derived, such as periodic solutions of rational form, solitary wave solutions of rational form, and so on.
基金the State Key Programme of Basic Research of China under，高等学校博士学科点专项科研项目
文摘The Jacobi elliptic function expansion method is extended to derive the explicit periodic wave solutions for nonlinear differential-difference equations. Three well-known examples are chosen to illustrate the application of the Jacobi elliptic function expansion method. As a result, three types of periodic wave solutions including Jacobi elliptic sine function, Jacobi elliptic cosine function and the third elliptic function solutions are obtained. It is shown that the shock wave solutions and solitary wave solutions can be obtained at their limit condition.
文摘The elliptic equation is taken as a transformation and applied to solve nonlinear wave equations. It is shown that this method is more powerful to give more kinds of solutions, such as rational solutions, solitary wave solutions,periodic wave solutions and so on, so it can be taken as a generalized method.
基金The project supported by National Natural Science Foundation of China under Grant No. 10575082
文摘Based on the multi-linear variable separation approach, a class of exact, doubly periodic wave solutions for the （3＋1）-dimensional Jimbo-Miwa equation is analytically obtained by choosing the Jacobi elliptic functions and their combinations. Limit cases are considered and some new solitary structures （new dromions） are derived. The interaction properties of periodic waves are numerically studied and found to be inelastic. Under long wave limit, two sets of new solution structures （dromions） are given. The interaction properties of these solutions reveal that some of them are completely elastic and some are inelastic.
文摘An extended hyperbola function method is proposed to construct exact solitary wave solutions to nonlinear wave equation based upon a coupled Riccati equation. It is shown that more new solitary wave solutions can be found by this new method, which include kink-shaped soliton solutions, bell-shaped soliton solutions and new solitary wave.The new method can be applied to other nonlinear equations in mathematical physics.
