The prolongation structure methodologies of Wahlquist-Estabrook [H.D. Wahlquist and F.B. Estabrook, J. Math. Phys. 16 （1975） 1] for nonlinear differential equations are applied to a more general set of coupled integ...The prolongation structure methodologies of Wahlquist-Estabrook [H.D. Wahlquist and F.B. Estabrook, J. Math. Phys. 16 （1975） 1] for nonlinear differential equations are applied to a more general set of coupled integrable dispersionless system. Based on the obtained prolongation structure, a Lie-Algebra valued connection of a closed ideal of exterior differential forms related to the above system is constructed. A Lie-Algebra representation of some hidden structural symmetries of the previous system, its Biicklund transformation using the Riccati form of the linear eigenvalue problem and their general corresponding Lax-representation are derived. In the wake of the previous results, we extend the above prolongation scheme to higher-dimensional systems from which a new （2 ＋ 1）-dimensional coupled integrable dispersionless system is unveiled along with its inverse scattering formulation, which applications are straightforward in nonlinear optics where additional propagating dimension deserves some attention.展开更多
In the wake of the recent investigation of new coupled integrable dispersionless equations by means of the Darboux transformation [Zhaqilao,et al.,Chin.Phys.B 18(2009) 1780],we carry out the initial value analysis of ...In the wake of the recent investigation of new coupled integrable dispersionless equations by means of the Darboux transformation [Zhaqilao,et al.,Chin.Phys.B 18(2009) 1780],we carry out the initial value analysis of the previous system using the fourth-order Runge-Kutta's computational scheme.As a result,while depicting its phase portraits accordingly,we show that the above dispersionless system actually supports two kinds of solutions amongst which the localized traveling wave-guide channels.In addition,paying particular interests to such localized structures,we construct the bilinear transformation of the current system from which scattering amongst the above waves can be deeply studied.展开更多
Based upon the group theoretical jet bundle formalism introduced by Wahlquist and Estabrook for discussing the complete integrability of soliton systems,we investigate the prolongation structure of Wadati-Konno-Ichika...Based upon the group theoretical jet bundle formalism introduced by Wahlquist and Estabrook for discussing the complete integrability of soliton systems,we investigate the prolongation structure of Wadati-Konno-Ichikawa isospectral evolution equations.As a result,we unearth a new physical coupled system entailing a hidden structural symmetry SL(3,R) arising in the description of ultra-short pulse propagation in optical nonlinear media.As a matter of fact,we depict a graphical representation of one-breather and two-breather ultra-short pulses in motion with a non-zero angular momentum.By extending the previous study to multidimensional symmetry SL(n,R),we unearth a more general class of multicomponent coupled nonlinear ultra-short pulse system with its associated inverse scattering formulation particularly useful in soliton theory.展开更多
We carry out the hidden structural symmetries embedded within a system comprising ultra-short pulses which propagate in optical nonlinear media.Based upon the Wahlquist Estabrook approach,we construct the Liealgebra v...We carry out the hidden structural symmetries embedded within a system comprising ultra-short pulses which propagate in optical nonlinear media.Based upon the Wahlquist Estabrook approach,we construct the Liealgebra valued connections associated to the previous symmetries while deriving their corresponding Lax-pairs,which are particularly useful in soliton theory.In the wake of previous results,we extend the above prolongation scheme to higher-dimensional systems from which a new (2+ 1)-dimensional ultra-short pulse equation is unveiled along with its inverse scattering formulation,the application of which are straightforward in nonlinear optics where an additional propagating dimension deserves some attention.展开更多
Based upon the powerful Hirota method for unearthing soliton solutions to nonlinear partial differential evolution equations,we investigate the scattering properties of a new coupled integrable dispersionless system w...Based upon the powerful Hirota method for unearthing soliton solutions to nonlinear partial differential evolution equations,we investigate the scattering properties of a new coupled integrable dispersionless system while surveying the interactions between its self-confined travelling wave solutions.As a result,we ascertain three types of scattering features depending strongly upon a characteristic parameter.Using such findings to depict soliton solutions with nonzero angular momenta,we derive an extended form of the dispersionless system,which is valuable for further physical applications.展开更多
文摘The prolongation structure methodologies of Wahlquist-Estabrook [H.D. Wahlquist and F.B. Estabrook, J. Math. Phys. 16 （1975） 1] for nonlinear differential equations are applied to a more general set of coupled integrable dispersionless system. Based on the obtained prolongation structure, a Lie-Algebra valued connection of a closed ideal of exterior differential forms related to the above system is constructed. A Lie-Algebra representation of some hidden structural symmetries of the previous system, its Biicklund transformation using the Riccati form of the linear eigenvalue problem and their general corresponding Lax-representation are derived. In the wake of the previous results, we extend the above prolongation scheme to higher-dimensional systems from which a new （2 ＋ 1）-dimensional coupled integrable dispersionless system is unveiled along with its inverse scattering formulation, which applications are straightforward in nonlinear optics where additional propagating dimension deserves some attention.
文摘In the wake of the recent investigation of new coupled integrable dispersionless equations by means of the Darboux transformation [Zhaqilao,et al.,Chin.Phys.B 18(2009) 1780],we carry out the initial value analysis of the previous system using the fourth-order Runge-Kutta's computational scheme.As a result,while depicting its phase portraits accordingly,we show that the above dispersionless system actually supports two kinds of solutions amongst which the localized traveling wave-guide channels.In addition,paying particular interests to such localized structures,we construct the bilinear transformation of the current system from which scattering amongst the above waves can be deeply studied.
文摘Based upon the group theoretical jet bundle formalism introduced by Wahlquist and Estabrook for discussing the complete integrability of soliton systems,we investigate the prolongation structure of Wadati-Konno-Ichikawa isospectral evolution equations.As a result,we unearth a new physical coupled system entailing a hidden structural symmetry SL(3,R) arising in the description of ultra-short pulse propagation in optical nonlinear media.As a matter of fact,we depict a graphical representation of one-breather and two-breather ultra-short pulses in motion with a non-zero angular momentum.By extending the previous study to multidimensional symmetry SL(n,R),we unearth a more general class of multicomponent coupled nonlinear ultra-short pulse system with its associated inverse scattering formulation particularly useful in soliton theory.
文摘We carry out the hidden structural symmetries embedded within a system comprising ultra-short pulses which propagate in optical nonlinear media.Based upon the Wahlquist Estabrook approach,we construct the Liealgebra valued connections associated to the previous symmetries while deriving their corresponding Lax-pairs,which are particularly useful in soliton theory.In the wake of previous results,we extend the above prolongation scheme to higher-dimensional systems from which a new (2+ 1)-dimensional ultra-short pulse equation is unveiled along with its inverse scattering formulation,the application of which are straightforward in nonlinear optics where an additional propagating dimension deserves some attention.
文摘Based upon the powerful Hirota method for unearthing soliton solutions to nonlinear partial differential evolution equations,we investigate the scattering properties of a new coupled integrable dispersionless system while surveying the interactions between its self-confined travelling wave solutions.As a result,we ascertain three types of scattering features depending strongly upon a characteristic parameter.Using such findings to depict soliton solutions with nonzero angular momenta,we derive an extended form of the dispersionless system,which is valuable for further physical applications.
