By means of the homogeneous balance principle, a nonlinear transformation to the well known breaking soliton equation with physical interest was given. The original equation was turned into a homogeneity differential...By means of the homogeneous balance principle, a nonlinear transformation to the well known breaking soliton equation with physical interest was given. The original equation was turned into a homogeneity differential equation with this nonlinear transformation. By solving the homogeneity equation via the simplified Hirota method and applying the nonlinear transformation, one soliton, two soliton and three soliton solutions as well as some other types of explicit solutions to the breaking soliton equation were obtained with the assistance of Maple.展开更多
In this paper,a new eighth-order(1+1)-dimensional time-dependent extended KdV equation has been developed.This considered equation is being found completely integrable by using the Painlevéanalysis method.Moreove...In this paper,a new eighth-order(1+1)-dimensional time-dependent extended KdV equation has been developed.This considered equation is being found completely integrable by using the Painlevéanalysis method.Moreover,three auto-Bäcklund transformations have been generated by truncating the Painlevéseries at a constant level.These auto-Bäcklund transformations have been used to derive various analytic solution families for the newly developed equation.These solutions include the kink-antikink soliton,kink-soliton,antikink-soliton,periodic-soliton,complex kink-soliton and complex periodic-soliton solutions.Multi-soliton solutions including N-soliton solution,have been obtained by using the simplified Hirota’s method for the considered equation.All the results are being expressed graphically to signify the physical importance of the considered equation.展开更多
文摘By means of the homogeneous balance principle, a nonlinear transformation to the well known breaking soliton equation with physical interest was given. The original equation was turned into a homogeneity differential equation with this nonlinear transformation. By solving the homogeneity equation via the simplified Hirota method and applying the nonlinear transformation, one soliton, two soliton and three soliton solutions as well as some other types of explicit solutions to the breaking soliton equation were obtained with the assistance of Maple.
文摘In this paper,a new eighth-order(1+1)-dimensional time-dependent extended KdV equation has been developed.This considered equation is being found completely integrable by using the Painlevéanalysis method.Moreover,three auto-Bäcklund transformations have been generated by truncating the Painlevéseries at a constant level.These auto-Bäcklund transformations have been used to derive various analytic solution families for the newly developed equation.These solutions include the kink-antikink soliton,kink-soliton,antikink-soliton,periodic-soliton,complex kink-soliton and complex periodic-soliton solutions.Multi-soliton solutions including N-soliton solution,have been obtained by using the simplified Hirota’s method for the considered equation.All the results are being expressed graphically to signify the physical importance of the considered equation.
