The Painlevé property for a(2+1)-dimensional Korteweg–de Vries(KdV) extension, the combined KP3(Kadomtsev–Petviashvili) and KP4(cKP3-4), is proved by using Kruskal’s simplification. The truncated Painlevé...The Painlevé property for a(2+1)-dimensional Korteweg–de Vries(KdV) extension, the combined KP3(Kadomtsev–Petviashvili) and KP4(cKP3-4), is proved by using Kruskal’s simplification. The truncated Painlevé expansion is used to find the Schwartz form, the Bäcklund/Levi transformations, and the residual nonlocal symmetry. The residual symmetry is localized to find its finite Bäcklund transformation. The local point symmetries of the model constitute a centerless Kac–Moody–Virasoro algebra. The local point symmetries are used to find the related group-invariant reductions including a new Lax integrable model with a fourth-order spectral problem. The finite transformation theorem or the Lie point symmetry group is obtained by using a direct method.展开更多
This article considers time-dependent variable coefficients(2+1)and(3+1)-dimensional extended Sakovich equation.Painlevéanalysis and auto-Bäcklund transformation methods are used to examine both the consider...This article considers time-dependent variable coefficients(2+1)and(3+1)-dimensional extended Sakovich equation.Painlevéanalysis and auto-Bäcklund transformation methods are used to examine both the considered equations.Painlevéanalysis is appeared to test the integrability while an auto-Bäcklund transformation method is being presented to derive new analytic soliton solution families for both the considered equations.Two new family of exact analytical solutions are being obtained success-fully for each of the considered equations.The soliton solutions in the form of rational and exponential functions are being depicted.The results are also expressed graphically to illustrate the potential and physical behaviour of both equations.Both the considered equations have applications in ocean wave theory as they depict new solitary wave soliton solutions by 3D and 2D graphs.展开更多
In this paper,we consider the(2+1)-dimensional Chaffee-Infante equation,which occurs in the fields of fluid dynamics,high-energy physics,electronic science etc.We build Bäcklund transformations and residual symme...In this paper,we consider the(2+1)-dimensional Chaffee-Infante equation,which occurs in the fields of fluid dynamics,high-energy physics,electronic science etc.We build Bäcklund transformations and residual symmetries in nonlocal structure using the Painlevétruncated expansion approach.We use a prolonged system to localize these symmetries and establish the associated one-parameter Lie transformation group.In this transformation group,we deliver new exact solution profiles via the combination of various simple(seed and tangent hyperbolic form)exact solution structures.In this manner,we acquire an infinite amount of exact solution forms methodically.Furthermore,we demonstrate that the model may be integrated in terms of consistent Riccati expansion.Using the Maple symbolic program,we derive the exact solution forms of solitary-wave and soliton-cnoidal interaction.Through 3D and 2D illustrations,we observe the dynamic analysis of the acquired solution forms.展开更多
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11975131 and 11435005)the K C Wong Magna Fund in Ningbo University。
文摘The Painlevé property for a(2+1)-dimensional Korteweg–de Vries(KdV) extension, the combined KP3(Kadomtsev–Petviashvili) and KP4(cKP3-4), is proved by using Kruskal’s simplification. The truncated Painlevé expansion is used to find the Schwartz form, the Bäcklund/Levi transformations, and the residual nonlocal symmetry. The residual symmetry is localized to find its finite Bäcklund transformation. The local point symmetries of the model constitute a centerless Kac–Moody–Virasoro algebra. The local point symmetries are used to find the related group-invariant reductions including a new Lax integrable model with a fourth-order spectral problem. The finite transformation theorem or the Lie point symmetry group is obtained by using a direct method.
文摘This article considers time-dependent variable coefficients(2+1)and(3+1)-dimensional extended Sakovich equation.Painlevéanalysis and auto-Bäcklund transformation methods are used to examine both the considered equations.Painlevéanalysis is appeared to test the integrability while an auto-Bäcklund transformation method is being presented to derive new analytic soliton solution families for both the considered equations.Two new family of exact analytical solutions are being obtained success-fully for each of the considered equations.The soliton solutions in the form of rational and exponential functions are being depicted.The results are also expressed graphically to illustrate the potential and physical behaviour of both equations.Both the considered equations have applications in ocean wave theory as they depict new solitary wave soliton solutions by 3D and 2D graphs.
基金Supported by the National Natural Science Foundation of China under Grant 61072145the Scientific Research Project of Beijing Educational Committee(SQKM201211232016)Beijing Excellent Talent Training Project(2013D005007000003)
文摘In this paper,we consider the(2+1)-dimensional Chaffee-Infante equation,which occurs in the fields of fluid dynamics,high-energy physics,electronic science etc.We build Bäcklund transformations and residual symmetries in nonlocal structure using the Painlevétruncated expansion approach.We use a prolonged system to localize these symmetries and establish the associated one-parameter Lie transformation group.In this transformation group,we deliver new exact solution profiles via the combination of various simple(seed and tangent hyperbolic form)exact solution structures.In this manner,we acquire an infinite amount of exact solution forms methodically.Furthermore,we demonstrate that the model may be integrated in terms of consistent Riccati expansion.Using the Maple symbolic program,we derive the exact solution forms of solitary-wave and soliton-cnoidal interaction.Through 3D and 2D illustrations,we observe the dynamic analysis of the acquired solution forms.
