As a new subject, soliton theory is shown to be an effective tool for describing and explaining nonlinear phenomena in nonlinear optics, super conductivity, plasma physics, magnetic fluid, etc. Thus, the study of soli...As a new subject, soliton theory is shown to be an effective tool for describing and explaining nonlinear phenomena in nonlinear optics, super conductivity, plasma physics, magnetic fluid, etc. Thus, the study of soliton equations has always been one of the most prominent events in the field of nonlinear science during the past few years. Moreover, it is important to seek the lattice soliton equation and study its properties. In this study, firstly, we derive a discrete integrable system by using the Tu model. Then, some properties of the obtained equation hierarchies are discussed.展开更多
Considering the integrable properties for the coupled equations, the variable-coefficient N- coupled nonlinear Schrodinger equations are under investigation analytically in this paper. Based on the Lax pair with the n...Considering the integrable properties for the coupled equations, the variable-coefficient N- coupled nonlinear Schrodinger equations are under investigation analytically in this paper. Based on the Lax pair with the nonisospectral parameter, a Backlund transformation for such a coupled system denoting in the F functions is constructed with the one-solitonic solution given as the application sample. Furthermore, an infinite number of conservation laws are obtained using symbolic computation.展开更多
With coming in force of The Law of Transformation of Areas at Disaster Risks numbered 16.5.2012/6306 by Ministry of Environment and Urbanization,the concept of urban transformation has entered to our life in Turkey.Ge...With coming in force of The Law of Transformation of Areas at Disaster Risks numbered 16.5.2012/6306 by Ministry of Environment and Urbanization,the concept of urban transformation has entered to our life in Turkey.Gentrification as one of the forms of urban transformation brought the existence of liberated zones produced by neo-liberal mentality.Sulukule area(Neslisah Sultan settlement)which is subject to research is counted among“the areas to be renewed and to be put under preservation”by numbered 2006/10299 decision of Council of Ministers.Due to the shortage of lands in the city,it is observed especially in 1980s that the families in high-income group have preferred to live in horizontally expending villa towns far from the center.While these residential areas are deepening the distance from the center in time,the pressure of housing demand of middle-income people and rent circles who are not planning to leave the city center caused to have an eye on these areas which are residential areas of mostly low-income people and appeared in certain regions as they are established without infrastructure and healthy conditions.With this law,the transformation has started in the areas such as Fikirtepe,Dolapdere,Esenler,and Banks of Halic(Golden Horn)where structural life is completed,and floor area ratio has been raised to 4.0 from 2.07.Vertical housing is stimulated by adding the street between the parcels to the blocks,it has been tried to prevent the victimization of local people to unearned income.There are some quarters that,under the name of gentrification,Romany citizens who passed to permanent settlement from nomadic culture at the Ottoman era,and who are engaged in activities such as handicraft,adornments,shoe making,weaving beside the show business at Fatih Sulukule district are convicted to lodge in the houses built in suburban if they have title deed,and in jerry-built tents if they don’t have deed.Chamber of Architects,Chamber of City Planners Istanbul Branch and Roma Culture Development and Solidari展开更多
With the help of the extended binary Bell polynomials, the new bilinear representations, Backlund trans- formations, Lax pair and infinite conservation laws for two types of variable-coefficient nonlinear integrable e...With the help of the extended binary Bell polynomials, the new bilinear representations, Backlund trans- formations, Lax pair and infinite conservation laws for two types of variable-coefficient nonlinear integrable equations are obtained, respectively, which are more straightforward than previous corresponding results obtained. Finally, we obtain new multi-soliton wave solutions of a reduced soliton equations with variable coefficients.展开更多
In this work,we study a generalized double dispersion Boussinesq equation that plays a significant role in fluid mechanics,scientific fields,and ocean engineering.This equation will be reduced to the Korteweg-de Vries...In this work,we study a generalized double dispersion Boussinesq equation that plays a significant role in fluid mechanics,scientific fields,and ocean engineering.This equation will be reduced to the Korteweg-de Vries equation via using the perturbation analysis.We derive the corresponding vectors,symmetry reduction and explicit solutions for this equation.We readily obtain Bäcklund transformation associated with truncated Painlevéexpansion.We also examine the related conservation laws of this equation via using the multiplier method.Moreover,we investigate the reciprocal Bäcklund transformations of the derived conservation laws for the first time.展开更多
文摘As a new subject, soliton theory is shown to be an effective tool for describing and explaining nonlinear phenomena in nonlinear optics, super conductivity, plasma physics, magnetic fluid, etc. Thus, the study of soliton equations has always been one of the most prominent events in the field of nonlinear science during the past few years. Moreover, it is important to seek the lattice soliton equation and study its properties. In this study, firstly, we derive a discrete integrable system by using the Tu model. Then, some properties of the obtained equation hierarchies are discussed.
基金Supported by the Foundation of Beijing Information Science and Technology University (Grant No. 1025020)Scientific Research Project of Beijing Educational Committee (Grant No. SQKM201211232016)+3 种基金Natural Science Foundation of Beijing (Grant No. 1102018)National Natural Science Foundation of China (Grant No. 61072145)Key Project of Chinese Ministry of Education (Grant No. 106033)National Basic Research Program of China (973 Program) (Grant No. 2005CB321901)
文摘Considering the integrable properties for the coupled equations, the variable-coefficient N- coupled nonlinear Schrodinger equations are under investigation analytically in this paper. Based on the Lax pair with the nonisospectral parameter, a Backlund transformation for such a coupled system denoting in the F functions is constructed with the one-solitonic solution given as the application sample. Furthermore, an infinite number of conservation laws are obtained using symbolic computation.
文摘With coming in force of The Law of Transformation of Areas at Disaster Risks numbered 16.5.2012/6306 by Ministry of Environment and Urbanization,the concept of urban transformation has entered to our life in Turkey.Gentrification as one of the forms of urban transformation brought the existence of liberated zones produced by neo-liberal mentality.Sulukule area(Neslisah Sultan settlement)which is subject to research is counted among“the areas to be renewed and to be put under preservation”by numbered 2006/10299 decision of Council of Ministers.Due to the shortage of lands in the city,it is observed especially in 1980s that the families in high-income group have preferred to live in horizontally expending villa towns far from the center.While these residential areas are deepening the distance from the center in time,the pressure of housing demand of middle-income people and rent circles who are not planning to leave the city center caused to have an eye on these areas which are residential areas of mostly low-income people and appeared in certain regions as they are established without infrastructure and healthy conditions.With this law,the transformation has started in the areas such as Fikirtepe,Dolapdere,Esenler,and Banks of Halic(Golden Horn)where structural life is completed,and floor area ratio has been raised to 4.0 from 2.07.Vertical housing is stimulated by adding the street between the parcels to the blocks,it has been tried to prevent the victimization of local people to unearned income.There are some quarters that,under the name of gentrification,Romany citizens who passed to permanent settlement from nomadic culture at the Ottoman era,and who are engaged in activities such as handicraft,adornments,shoe making,weaving beside the show business at Fatih Sulukule district are convicted to lodge in the houses built in suburban if they have title deed,and in jerry-built tents if they don’t have deed.Chamber of Architects,Chamber of City Planners Istanbul Branch and Roma Culture Development and Solidari
基金Supported by the Fundamental Research Funds for the Central Universities under Grant Nos. 20BXK03 and 2012LWB51
文摘With the help of the extended binary Bell polynomials, the new bilinear representations, Backlund trans- formations, Lax pair and infinite conservation laws for two types of variable-coefficient nonlinear integrable equations are obtained, respectively, which are more straightforward than previous corresponding results obtained. Finally, we obtain new multi-soliton wave solutions of a reduced soliton equations with variable coefficients.
基金supported by Natural Science Foundation of Hebei Province,China(Grant No.A2018207030)Youth Key Program of Hebei University of Economics and Business(2018QZ07)+2 种基金Key Program of Hebei University of Economics and Business(2020ZD11)Youth Team Support Program of Hebei University of Economics and BusinessNational Natural Science Foundation of China(Grant No.11801133)。
文摘In this work,we study a generalized double dispersion Boussinesq equation that plays a significant role in fluid mechanics,scientific fields,and ocean engineering.This equation will be reduced to the Korteweg-de Vries equation via using the perturbation analysis.We derive the corresponding vectors,symmetry reduction and explicit solutions for this equation.We readily obtain Bäcklund transformation associated with truncated Painlevéexpansion.We also examine the related conservation laws of this equation via using the multiplier method.Moreover,we investigate the reciprocal Bäcklund transformations of the derived conservation laws for the first time.
