Having realized various significant roles that higher-dimensional nonlinear partial differ-ential equations(NLPDEs)play in engineering,we analytically investigate in this paper,a higher-dimensional soliton equation,wi...Having realized various significant roles that higher-dimensional nonlinear partial differ-ential equations(NLPDEs)play in engineering,we analytically investigate in this paper,a higher-dimensional soliton equation,with applications particularly in ocean physics and mechatronics(electrical electronics and mechanical)engineering.Infinitesimal generators of Lie point symmetries of the equation are computed using Lie group analysis of differen-tial equations.In addition,we construct commutation as well as Lie adjoint representation tables for the nine-dimensional Lie algebra achieved.Further,a one-dimensional optimal system of Lie subalgebras is also presented for the soliton equation.This consequently enables us to generate abundant group-invariant solutions through the reduction of the understudy equation into various ordinary differential equations(ODEs).On solving the achieved nonlinear differential equations,we secure various solitonic solutions.In conse-quence,these solutions containing diverse mathematical functions furnish copious shapes of dynamical wave structures,ranging from periodic,kink and kink-shaped nanopteron,soliton(bright and dark)to breather waves with extensive wave collisions depicted.We physically interpreted the resulting soliton solutions by imploring graphical depictions in three dimensions,two dimensions and density plots.Moreover,the gained group-invariant solutions involved several arbitrary functions,thus exhibiting rich physical structures.We also implore the power series technique to solve part of the complicated differential equa-tions and give valid comments on their results.Later,we outline some applications of our results in ocean physics and mechatronics engineering.展开更多
The derivation of nonlinear integrable evolution partial differential equations in higher dimensions has always been the holy grail in the field of integrability.The well-known modified Kd V equation is a prototypical...The derivation of nonlinear integrable evolution partial differential equations in higher dimensions has always been the holy grail in the field of integrability.The well-known modified Kd V equation is a prototypical example of an integrable evolution equation in one spatial dimension.Do there exist integrable analogs of the modified Kd V equation in higher spatial dimensions?In what follows,we present a positive answer to this question.In particular,rewriting the(1+1)-dimensional integrable modified Kd V equation in conservation forms and adding deformation mappings during the process allows one to construct higher-dimensional integrable equations.Further,we illustrate this idea with examples from the modified Kd V hierarchy and also present the Lax pairs of these higher-dimensional integrable evolution equations.展开更多
The work is devoted to the fractional characterization of time-dependent coupled convection-diffusion systems arising in magnetohydrodynamics(MHD)flows.The time derivative is expressed by means of Caputo’s fractional...The work is devoted to the fractional characterization of time-dependent coupled convection-diffusion systems arising in magnetohydrodynamics(MHD)flows.The time derivative is expressed by means of Caputo’s fractional derivative concept,while the model is solved via the full-spectral method(FSM)and the semi-spectral scheme(SSS).The FSM is based on the operational matrices of derivatives constructed by using higher-order orthogonal polynomials and collocation techniques.The SSS is developed by discretizing the time variable,and the space domain is collocated by using equal points.A detailed comparative analysis is made through graphs for various parameters and tables with existing literature.The contour graphs are made to show the behaviors of the velocity and magnetic fields.The proposed methods are reasonably efficient in examining the behavior of convection-diffusion equations arising in MHD flows,and the concept may be extended for variable order models arising in MHD flows.展开更多
ⅠIn the recent years, with the development of the superstring theory (requiring (1+9) dimensional space time) and the application of the Kaluza-Klein theory to the research of the very early phases of the universe (r...ⅠIn the recent years, with the development of the superstring theory (requiring (1+9) dimensional space time) and the application of the Kaluza-Klein theory to the research of the very early phases of the universe (requiring (1+10) dimensional space-time), higher-dimensional physics has assumed a high measure of importance. Emelyanov et al. have in detail evaluated the study situation on the higher-dimensional space-time.展开更多
We consider both gauged and ungauged minimal supergravities in five dimensions and analyse the charged rotating solutions with two equal angular momenta J.When the electric charge Q∼J^(2/3) with some specific coeffic...We consider both gauged and ungauged minimal supergravities in five dimensions and analyse the charged rotating solutions with two equal angular momenta J.When the electric charge Q∼J^(2/3) with some specific coefficient,we find new extremal black objects emerge that are asymptotic to either Minkowski or global AdS spacetimes and can be best described as degenerate black rings.Their near-horizon geometry is locally AdS3×S^(2),where the periodic U(1)fibre coordinate in S 3 untwists and collapses to be the degenerate part of the AdS3 horizon.It turns out that there are two branches of extremal rotating black holes,starting as the extremal RN black holes of the same mass,but opposite charges.With the increasing of the angular momentum,they will join to become the same degenerate black ring,where the Gibbs free energies however are not continuous at the joining.For the same Q(J)relation,we find that there is in addition a rotating soliton whose mass is smaller than that of the degenerate black ring.展开更多
基金the North-West University,Mafikeng campus for its continued support.
文摘Having realized various significant roles that higher-dimensional nonlinear partial differ-ential equations(NLPDEs)play in engineering,we analytically investigate in this paper,a higher-dimensional soliton equation,with applications particularly in ocean physics and mechatronics(electrical electronics and mechanical)engineering.Infinitesimal generators of Lie point symmetries of the equation are computed using Lie group analysis of differen-tial equations.In addition,we construct commutation as well as Lie adjoint representation tables for the nine-dimensional Lie algebra achieved.Further,a one-dimensional optimal system of Lie subalgebras is also presented for the soliton equation.This consequently enables us to generate abundant group-invariant solutions through the reduction of the understudy equation into various ordinary differential equations(ODEs).On solving the achieved nonlinear differential equations,we secure various solitonic solutions.In conse-quence,these solutions containing diverse mathematical functions furnish copious shapes of dynamical wave structures,ranging from periodic,kink and kink-shaped nanopteron,soliton(bright and dark)to breather waves with extensive wave collisions depicted.We physically interpreted the resulting soliton solutions by imploring graphical depictions in three dimensions,two dimensions and density plots.Moreover,the gained group-invariant solutions involved several arbitrary functions,thus exhibiting rich physical structures.We also implore the power series technique to solve part of the complicated differential equa-tions and give valid comments on their results.Later,we outline some applications of our results in ocean physics and mechatronics engineering.
基金sponsored by the National Natural Science Foundations of China(Nos.12235007,11975131,11435005,12275144,11975204)KC Wong Magna Fund in Ningbo UniversityNatural Science Foundation of Zhejiang Province No.LQ20A010009。
文摘The derivation of nonlinear integrable evolution partial differential equations in higher dimensions has always been the holy grail in the field of integrability.The well-known modified Kd V equation is a prototypical example of an integrable evolution equation in one spatial dimension.Do there exist integrable analogs of the modified Kd V equation in higher spatial dimensions?In what follows,we present a positive answer to this question.In particular,rewriting the(1+1)-dimensional integrable modified Kd V equation in conservation forms and adding deformation mappings during the process allows one to construct higher-dimensional integrable equations.Further,we illustrate this idea with examples from the modified Kd V hierarchy and also present the Lax pairs of these higher-dimensional integrable evolution equations.
基金Project supported by the National Natural Science Foundation of China(Nos.12250410244,11872151)the Jiangsu Province Education Development Special Project-2022 for Double First-ClassSchool Talent Start-up Fund of China(No.2022r109)the Longshan Scholar Program of Jiangsu Province of China。
文摘The work is devoted to the fractional characterization of time-dependent coupled convection-diffusion systems arising in magnetohydrodynamics(MHD)flows.The time derivative is expressed by means of Caputo’s fractional derivative concept,while the model is solved via the full-spectral method(FSM)and the semi-spectral scheme(SSS).The FSM is based on the operational matrices of derivatives constructed by using higher-order orthogonal polynomials and collocation techniques.The SSS is developed by discretizing the time variable,and the space domain is collocated by using equal points.A detailed comparative analysis is made through graphs for various parameters and tables with existing literature.The contour graphs are made to show the behaviors of the velocity and magnetic fields.The proposed methods are reasonably efficient in examining the behavior of convection-diffusion equations arising in MHD flows,and the concept may be extended for variable order models arising in MHD flows.
文摘ⅠIn the recent years, with the development of the superstring theory (requiring (1+9) dimensional space time) and the application of the Kaluza-Klein theory to the research of the very early phases of the universe (requiring (1+10) dimensional space-time), higher-dimensional physics has assumed a high measure of importance. Emelyanov et al. have in detail evaluated the study situation on the higher-dimensional space-time.
基金This work was supported by the National Natural Science Foundation of China(Grant Nos.11875200,and 11935009).
文摘We consider both gauged and ungauged minimal supergravities in five dimensions and analyse the charged rotating solutions with two equal angular momenta J.When the electric charge Q∼J^(2/3) with some specific coefficient,we find new extremal black objects emerge that are asymptotic to either Minkowski or global AdS spacetimes and can be best described as degenerate black rings.Their near-horizon geometry is locally AdS3×S^(2),where the periodic U(1)fibre coordinate in S 3 untwists and collapses to be the degenerate part of the AdS3 horizon.It turns out that there are two branches of extremal rotating black holes,starting as the extremal RN black holes of the same mass,but opposite charges.With the increasing of the angular momentum,they will join to become the same degenerate black ring,where the Gibbs free energies however are not continuous at the joining.For the same Q(J)relation,we find that there is in addition a rotating soliton whose mass is smaller than that of the degenerate black ring.
