In this paper,the bifurcation of solitary,kink,anti-kink,and periodic waves for （2＋1）-dimension nonlinear dispersive long wave equation is studied by using the bifurcation theory of planar dynamical systems.Bifurca...In this paper,the bifurcation of solitary,kink,anti-kink,and periodic waves for （2＋1）-dimension nonlinear dispersive long wave equation is studied by using the bifurcation theory of planar dynamical systems.Bifurcation parameter sets are shown,and under various parameter conditions,all exact explicit formulas of solitary travelling wave solutions and kink travelling wave solutions and periodic travelling wave solutions are listed.展开更多
The complete analytical solution of the Riemann problem for the homo-geneous Dispersive Nonlinear Shallow Water Equations [Antuono, Liapidevskii andBrocchini, Stud. Appl. Math., 122 (2009), pp. 1-28] is presented, for...The complete analytical solution of the Riemann problem for the homo-geneous Dispersive Nonlinear Shallow Water Equations [Antuono, Liapidevskii andBrocchini, Stud. Appl. Math., 122 (2009), pp. 1-28] is presented, for both wet-bed anddry-bed conditions. Moreover, such a set of hyperbolic and dispersive depth-averagedequations shows an interesting resonance phenomenon in the wave pattern of the solu-tion and we define conditions for the occurrence of resonance and present an algorithmto capture it. As an indirect check on the analytical solution we have carried out a de-tailed comparison with the numerical solution of the government equations obtainedfrom a dissipative method that does not make explicit use of the solution of the localRiemann problem.展开更多
By the use of an auxiliary equation, we find bright and dark optical soliton and other soliton solutions for the higher-order nonlinear Schrodinger equation (NLSE) with fourth-order dispersion (FOD), cubic-quintic ter...By the use of an auxiliary equation, we find bright and dark optical soliton and other soliton solutions for the higher-order nonlinear Schrodinger equation (NLSE) with fourth-order dispersion (FOD), cubic-quintic terms, self-steepening, and nonlinear dispersive terms. Moreover, we give the formation condition of the bright and dark solitons for this higher-order NLSE.展开更多
基金Supported by the National Natural Science Foundation of China (10871206)Program for Excellent Talents in Guangxi Higher Education Institutions
文摘In this paper,the bifurcation of solitary,kink,anti-kink,and periodic waves for （2＋1）-dimension nonlinear dispersive long wave equation is studied by using the bifurcation theory of planar dynamical systems.Bifurcation parameter sets are shown,and under various parameter conditions,all exact explicit formulas of solitary travelling wave solutions and kink travelling wave solutions and periodic travelling wave solutions are listed.
基金The authors acknowledge the partial financial support received by the E.U.through the INTAS Project 06-1000013-9236 and by the“Ministero Infrastrutture e Trasporti”within the“Programma di Ricerca 2007-2009”.Acknowledgments are also due to Prof.Maurizio Brocchini for his useful comments and suggestions.
文摘The complete analytical solution of the Riemann problem for the homo-geneous Dispersive Nonlinear Shallow Water Equations [Antuono, Liapidevskii andBrocchini, Stud. Appl. Math., 122 (2009), pp. 1-28] is presented, for both wet-bed anddry-bed conditions. Moreover, such a set of hyperbolic and dispersive depth-averagedequations shows an interesting resonance phenomenon in the wave pattern of the solu-tion and we define conditions for the occurrence of resonance and present an algorithmto capture it. As an indirect check on the analytical solution we have carried out a de-tailed comparison with the numerical solution of the government equations obtainedfrom a dissipative method that does not make explicit use of the solution of the localRiemann problem.
文摘By the use of an auxiliary equation, we find bright and dark optical soliton and other soliton solutions for the higher-order nonlinear Schrodinger equation (NLSE) with fourth-order dispersion (FOD), cubic-quintic terms, self-steepening, and nonlinear dispersive terms. Moreover, we give the formation condition of the bright and dark solitons for this higher-order NLSE.
