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Positon and hybrid solutions for the(2+1)-dimensional complex modified Korteweg-de Vries equations 被引量:1
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作者 袁丰 Behzad Ghanbari 《Chinese Physics B》 SCIE EI CAS CSCD 2023年第4期118-124,共7页
Solving nonlinear partial differential equations have attracted intensive attention in the past few decades. In this paper, the Darboux transformation method is used to derive several positon and hybrid solutions for ... Solving nonlinear partial differential equations have attracted intensive attention in the past few decades. In this paper, the Darboux transformation method is used to derive several positon and hybrid solutions for the(2+1)-dimensional complex modified Korteweg–de Vries equations. Based on the zero seed solution, the positon solution and the hybrid solutions of positon and soliton are constructed. The composition of positons is studied, showing that multi-positons of(2+1)-dimensional equations are decomposed into multi-solitons as well as the(1+1)-dimensions. Moreover, the interactions between positon and soliton are analyzed. In addition, the hybrid solutions of b-positon and breather are obtained using the plane wave seed solution, and their evolutions with time are discussed. 展开更多
关键词 positon solution b-positon solution breather solution the hybrid solution the Darboux transformation
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General M-lumps, T-breathers, and hybrid solutions to (2+1)-dimensional generalized KDKK equation 被引量:1
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作者 Peisen Yuan Jiaxin Qi +1 位作者 Ziliang Li Hongli An 《Chinese Physics B》 SCIE EI CAS CSCD 2021年第4期173-183,共11页
A special transformation is introduced and thereby leads to the N-soliton solution of the(2+1)-dimensional generalized Konopelchenko-Dubrovsky-Kaup-Kupershmidt(KDKK) equation.Then,by employing the long wave limit and ... A special transformation is introduced and thereby leads to the N-soliton solution of the(2+1)-dimensional generalized Konopelchenko-Dubrovsky-Kaup-Kupershmidt(KDKK) equation.Then,by employing the long wave limit and imposing complex conjugate constraints to the related solitons,various localized interaction solutions are constructed,including the general M-lumps,T-breathers,and hybrid wave solutions.Dynamical behaviors of these solutions are investigated analytically and graphically.The solutions obtained are very helpful in studying the interaction phenomena of nonlinear localized waves.Therefore,we hope these results can provide some theoretical guidance to the experts in oceanography,atmospheric science,and weather forecasting. 展开更多
关键词 KDKK equation Hirota bilinear method high-order lump solution T-breather solution hybrid solution
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High-Order Soliton Solutions and Hybrid Behavior for the (2 + 1)-Dimensional Konopelchenko-Dubrovsky Equations
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作者 Xingying Li Yin Ji 《Journal of Applied Mathematics and Physics》 2024年第7期2452-2466,共15页
In this paper, the evolutionary behavior of N-solitons for a (2 + 1)-dimensional Konopelchenko-Dubrovsky equations is studied by using the Hirota bilinear method and the long wave limit method. Based on the N-soliton ... In this paper, the evolutionary behavior of N-solitons for a (2 + 1)-dimensional Konopelchenko-Dubrovsky equations is studied by using the Hirota bilinear method and the long wave limit method. Based on the N-soliton solution, we first study the evolution from N-soliton to T-order (T=1,2) breather wave solutions via the paired-complexification of parameters, and then we get the N-order rational solutions, M-order (M=1,2) lump solutions, and the hybrid behavior between a variety of different types of solitons combined with the parameter limit technique and the paired-complexification of parameters. Meanwhile, we also provide a large number of three-dimensional figures in order to better show the degeneration of the N-soliton and the interaction behavior between different N-solitons. 展开更多
关键词 Konopelchenko-Dubrovsky Equations Hirota Bilinear Method M-Order Lump solutions High-Order hybrid solutions Interaction Behavior
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High-Order Solitons and Hybrid Behavior of (3 + 1)-Dimensional Potential Yu-Toda-Sasa-Fukuyama Equation with Variable Coefficients
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作者 Xiyu Tan Xingying Li 《Journal of Applied Mathematics and Physics》 2024年第8期2738-2763,共26页
In this paper, some exact solutions of the (3 + 1)-dimensional variable-coefficient Yu-Toda-Sasa-Fukuyama equation are investigated. By using Hirota’s direct method and symbolic computation, we obtained N-soliton sol... In this paper, some exact solutions of the (3 + 1)-dimensional variable-coefficient Yu-Toda-Sasa-Fukuyama equation are investigated. By using Hirota’s direct method and symbolic computation, we obtained N-soliton solution. By using the long wave limit method, the N-order rational solution can be obtained from N-order soliton solution. Then, through the paired complexification of parameters, the lump solution is obtained from N-order rational solution. Meanwhile, we obtained a hybrid solution between 1-lump solution and N-soliton (N=1,2) by using the long wave limit method and parameter complex. Furthermore, four different sets of three-dimensional graphs of solitons, lump solutions and hybrid solutions are drawn by selecting four different sets of coefficient functions which include one set of constant coefficient function and three sets of variable coefficient functions. 展开更多
关键词 Variable-Coefficient YTSF Equation Hirota Bilinear Method N-SOLITON hybrid Solution
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Resonance Y-type soliton solutions and some new types of hybrid solutions in the(2+1)-dimensional Sawada–Kotera equation 被引量:3
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作者 Jiaheng Li Qingqing Chen Biao Li 《Communications in Theoretical Physics》 SCIE CAS CSCD 2021年第4期52-57,共6页
In this paper,based on N-soliton solutions,we introduce a new constraint among parameters to find the resonance Y-type soliton solutions in(2+1)-dimensional integrable systems.Then,we take the(2+1)-dimensional Sawada... In this paper,based on N-soliton solutions,we introduce a new constraint among parameters to find the resonance Y-type soliton solutions in(2+1)-dimensional integrable systems.Then,we take the(2+1)-dimensional Sawada–Kotera equation as an example to illustrate how to generate these resonance Y-type soliton solutions with this new constraint.Next,by the long wave limit method,velocity resonance and module resonance,we can obtain some new types of hybrid solutions of resonance Y-type solitons with line waves,breather waves,high-order lump waves respectively.Finally,we also study the dynamics of these interaction solutions and indicate mathematically that these interactions are elastic. 展开更多
关键词 resonance Y-type solitons (2+1)-dimensional Sawada-Kotera equation hybrid solutions
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Soliton molecules and some novel hybrid solutions for the(2+1)-dimensional generalized Konopelchenko–Dubrovsky–Kaup–Kupershmidt equation
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作者 Hongcai Ma Qiaoxin Cheng Aiping Deng 《Communications in Theoretical Physics》 SCIE CAS CSCD 2020年第9期1-7,共7页
Soliton molecules have become one of the hot topics in recent years. In this article, we investigate soliton molecules and some novel hybrid solutions for the(2+1)-dimensional generalized Konopelchenko–Dubrovsky–Kau... Soliton molecules have become one of the hot topics in recent years. In this article, we investigate soliton molecules and some novel hybrid solutions for the(2+1)-dimensional generalized Konopelchenko–Dubrovsky–Kaup–Kupershmidt(gKDKK) equation by using the velocity resonance, module resonance, and long wave limits methods. By selecting some specific parameters, we can obtain soliton molecules and asymmetric soliton molecules of the gKDKK equation. And the interactions among N-soliton molecules are elastic. Furthermore, some novel hybrid solutions of the gKDKK equation can be obtained, which are composed of lumps,breathers, soliton molecules and asymmetric soliton molecules. Finally, the images of soliton molecules and some novel hybrid solutions are given, and their dynamic behavior is analyzed. 展开更多
关键词 the(2+1)-dimensional generalized Konopelchenko–Dubrovsky–Kaup–Kupershmidt equation soliton molecules hybrid solutions velocity resonance long-wave limit
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Trajectory equation of a lump before and after collision with other waves for generalized Hirota–Satsuma–Ito equation
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作者 夏亚荣 张开开 +1 位作者 姚若侠 申亚丽 《Chinese Physics B》 SCIE EI CAS CSCD 2023年第10期163-171,共9页
Based on the Hirota bilinear and long wave limit methods,the hybrid solutions of m-lump with n-soliton and nbreather wave for generalized Hirota–Satsuma–Ito(GHSI)equation are constructed.Then,by approximating soluti... Based on the Hirota bilinear and long wave limit methods,the hybrid solutions of m-lump with n-soliton and nbreather wave for generalized Hirota–Satsuma–Ito(GHSI)equation are constructed.Then,by approximating solutions of the GHSI equation along some parallel orbits at infinity,the trajectory equation of a lump wave before and after collisions with n-soliton and n-breather wave are studied,and the expressions of phase shift for lump wave before and after collisions are given.Furthermore,it is revealed that collisions between the lump wave and other waves are elastic,the corresponding collision diagrams are used to further explain. 展开更多
关键词 Hirota bilinear method long wave limit hybrid solutions trajectory equation
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Dynamic response of axially moving Timoshenko beams: integral transform solution 被引量:5
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作者 安晨 苏健 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2014年第11期1421-1436,共16页
The generalized integral transform technique (GITT) is used to find a semianalytical numerical solution for dynamic response of an axially moving Timoshenko beam with clamped-clamped and simply-supported boundary co... The generalized integral transform technique (GITT) is used to find a semianalytical numerical solution for dynamic response of an axially moving Timoshenko beam with clamped-clamped and simply-supported boundary conditions, respectively. The implementation of GITT approach for analyzing the forced vibration equation eliminates the space variable and leads to systems of second-order ordinary differential equations (ODEs) in time. The MATHEMATICA built-in function, NDSolve, is used to numerically solve the resulting transformed ODE system. The good convergence behavior of the suggested eigenfunction expansions is demonstrated for calculating the transverse deflection and the angle of rotation of the beam cross-section. Moreover, parametric studies are performed to analyze the effects of the axially moving speed, the axial tension, and the amplitude of external distributed force on the vibration amplitude of axially moving Timoshenko beams. 展开更多
关键词 axially moving Timoshenko beam transverse vibration integral transform hybrid solution
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Separation of contact stress components by moire interferometry 被引量:1
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作者 Ming Li Jue Zhang Chong Wu Jing Fang 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2007年第6期707-711,共5页
A hybrid technique of combining moire measurement and analytical solution is developed to separate the normal and the tangential components of distributed contact stresses between two co-plane bodies. The moire interf... A hybrid technique of combining moire measurement and analytical solution is developed to separate the normal and the tangential components of distributed contact stresses between two co-plane bodies. The moire interfe-rometry offers the displacement fields near the deformed contact zone, from which the tangential strains and boundary slopes of the deformed configurations can be evaluated. Those experimental results provide boundary conditions for the discrete integration of Flamant's solutions, to inversely compute the separated components of the contact stresses. 展开更多
关键词 Moire patterns Contact deformation Experimental/analytical hybrid solution
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Multisoliton solutions with even numbers and its generated solutions for nonlocal Fokas–Lenells equation 被引量:1
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作者 Rong Fan Zhao Zhang Biao Li 《Communications in Theoretical Physics》 SCIE CAS CSCD 2020年第12期94-98,共5页
In this letter,we investigate multisoliton solutions with even numbers and its generated solutions for nonlocal Fokas–Lenells equation over a nonzero background.First,we obtain 2 n-soliton solutions with a nonzero ba... In this letter,we investigate multisoliton solutions with even numbers and its generated solutions for nonlocal Fokas–Lenells equation over a nonzero background.First,we obtain 2 n-soliton solutions with a nonzero background via n-fold Darboux transformation,and find that these soliton solutions will appear in pairs.Particularly,2 n-soliton solutions consist of n‘bright’solitons and n‘dark’solitons.This phenomenon implies a new form of integrability:even integrability.Then interactions between solitons with even numbers and breathers are studied in detail.To our best knowledge,a novel nonlinear superposition between a kink and 2 n-soliton is also generated for the first time.Finally,interactions between some different smooth positons with a nonzero background are derived. 展开更多
关键词 2n-soliton positon solutions hybrid solutions
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URBAN FORM FOR A SUSTAINABLE FUTURE: How Sustainable Is Distributed Working in the Networked City?
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作者 John Worthington 《Journal of Green Building》 2009年第4期148-157,共10页
Our understanding of urban form depends on how we perceive the city.Much of the literature on urban form(1)has focused on the pre-industrial and industrial city,celebrating its compact form,contiguous functions and si... Our understanding of urban form depends on how we perceive the city.Much of the literature on urban form(1)has focused on the pre-industrial and industrial city,celebrating its compact form,contiguous functions and single dominant centre.More recently writings by Castels(2)and Soja(3)have described the dispersed,city of the post industrial era.This networked city triggered by the freedom afforded by the new technology(4)has exposed a new dimension to urban form.The model of the compact city advocated by those such as Lord Rogers Task Force for delivering the Urban Renaissance(5)is being questioned(6)and a new model of“high density nodes,in a high density landscape resulting in a low density city,”as in the Deltametropolis,described by Dirk Frieling(7).Compactness,cramming more development into the city and making public spaces of a higher density and quality,Rogers and Burdett argue(8)will make“urban living attractive,ecologically sustainable,economically strong and socially inclusive.”The alternative argument is that the economic success of cities is reliant on the networking of resources across a metropolitan region.Echenique argues(9)that cities disperse in their search for mobility and space.“Mobility increases the effi ciency of households and fi rms which in turn generates more income and profi ts.As income increases,so does the demand for space,residential and commercial alike.”Sustainability has become the current banner of political correctness.Sustainability however is a slippery word.It is easy to focus on one aspect and lose the value of its holistic meaning.For many architects“green buildings”equals a sustainable future.However,clever design solutions single-mindedly pursued with little regard to the wider exploration of the potential environmental savings that may be achieved through organisational innovation are only half the answer.A holistic approach concerned with both building and organisational design and focused on“lean thinking”(10)could make considerable inroads into reducing the ecological footprint.The paper draws on DEGW’s experience of advising major corporations and cities on strategies for managing the process of intensifi cation and change(11).It explores how major improvements might be gained in meeting our goals for the sustainable city through reconsidering the way we work and allocate space.The underlying proposition is that technology has offered us new opportunities which have changed our paradigm of living and working.This in turn has provided us with a new perception of the city,as a distributed series of high density centres connected by good public and private transport,within a low density landscape.The paper argues that considerable improvements in workplace sustainability can be achieved by applying a holistic approach.These may include a combination of strategies,from rethinking the organisation of work processes and the locations and time work is undertaken,to reducing the need for resources by a more intensive use of land and fl oor space.Disjointed,dispersed“urban sprawl”can be wasteful.The alternative emerging urban form is a planned,dispersed,“networked”city with well integrated public and private transport that yields greater choice of location and lifestyles so supporting social,economic and environmental sustainability. 展开更多
关键词 compact city networked economy dispersed polycentric city region overlapping functions signifi cant locations hubs nodes distinctive places shared settings core fl exi and on-demand space hybrid solutions
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General M-lump,high-order breather,and localized interaction solutions to(2+1)-dimensional generalized Bogoyavlensky-Konopelchenko equation
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作者 Hongcai MA Yunxiang BAI Aiping DENG 《Frontiers of Mathematics in China》 SCIE CSCD 2022年第5期943-960,共18页
The(2+1)-dimensional generalized Bogoyavlensky-Konopelchenko equation is a significant physical model.By using the long wave limit method and confining the conjugation conditions on the interrelated solitons,the gener... The(2+1)-dimensional generalized Bogoyavlensky-Konopelchenko equation is a significant physical model.By using the long wave limit method and confining the conjugation conditions on the interrelated solitons,the general M-lump,high-order breather,and localized interaction hybrid solutions are investigated,respectively.Then we implement the numerical simulations to research their dynamical behaviors,which indicate that different parameters have very different dynamic properties and propagation modes of the waves.The method involved can be validly employed to get high-order waves and study their propagation phenomena of many nonlinear equations. 展开更多
关键词 Bogoyavlensky-Konopelchenko equation long wave limit M-lump solution hybrid solution
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A review of the technologies for wave energy extraction 被引量:6
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作者 Eugen Rusu Florin Onea 《Clean Energy》 EI 2018年第1期10-19,共10页
The main objective of this article is to provide a comprehensive picture of existing wave technologies being used for wave energy extraction.The overview will explain their potential and also the challenges wave techn... The main objective of this article is to provide a comprehensive picture of existing wave technologies being used for wave energy extraction.The overview will explain their potential and also the challenges wave technologies face.The article will also briefly discuss the benefits of combined offshore wind-wave projects,also known as hybrids.Key factors and impacts on relevant existing wave technologies will be outlined,including capacity factor and capture width.Finally the levelized cost of energy(LCOE)targets for the most promising technologies will be discussed. 展开更多
关键词 wave power wave energy converters capacity factor capture width hybrid solutions
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Plug-in and plug-out dispatch optimization in microgrid clusters based on flexible communication 被引量:6
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作者 Jie YU Ming NI +1 位作者 Yiping JIAO Xiaolong WANG 《Journal of Modern Power Systems and Clean Energy》 SCIE EI 2017年第4期663-670,共8页
With large-scale development of distributed generation(DG) and its potential role in microgrids, the microgrid cluster(MGC) becomes a useful control model to assist the integration of DG. Considering that microgrids i... With large-scale development of distributed generation(DG) and its potential role in microgrids, the microgrid cluster(MGC) becomes a useful control model to assist the integration of DG. Considering that microgrids in a MGC, power dispatch optimization in a MGC is dif-ficult to achieve. In this paper, a hybrid interactive communication optimization solution(HICOS) is suggested based on flexible communication, which could be used to solve plug-in or plug-out operation states of microgrids in MGC power dispatch optimization. HICOS consists of a hierarchical architecture: the upper layer uses distributed control among multiple microgrids, with no central controller for the MGC, and the lower layer uses a central controller for each microgrid. Based on flexible communication links among microgrids, the optimal iterative information are exchanged among microgrids, thus HICOS would gradually converge to the global optimal solution.While some microgrids plug-in or plug-out, communication links will be changed, so as to unsuccessfully reach optimal solution. Differing from changeless communication links in traditional communication networks, HICOS redefines the topology of flexible communication links to meet the requirement to reach the global optimal solutions.Simulation studies show that HICOS could effectively reach the global optimal dispatch solution with non-MGC center. Especially, facing to microgrids plug-in or plug-out states, HICOS would also reach the global optimal solution based on refined communication link topology. 展开更多
关键词 Microgrid Cluster(MGC) Plug-in/plug-out dispatch optimization hybrid interactive communication optimization solution(HICOS) Flexible communication
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