Symmetries and Lie algebra of the differential-difference Kadomstev-Petviashvili hierarchy

By introducing suitable non-isospectral flows we construct two sets of symmetries for the isospectral differential-difference Kadomstev-Petviashvili hierarchy. The symmetries form an infinite dimensional Lie algebra.Comment: 9 page

Symmetry and double reduction for exact solutions of selected nonlinear partial differential equations

Amongst the several analytic methods available to obtain exact solutions of non-linear differential equations, Lie symmetry reduction and double reduction technique are proven to be most effective and have attracted researcher from different areas to utilize these methods in their research. In this research, Lie symmetry analysis and double reduction are used to find the exact solutions of nonlinear differential equations. For Lie symmetry reduction method, symmetries of differential equation will be obtained and hence invariants will be obtained, thus differential equation will be reduced and exact solutions are calculated. For the method of double reduction, we first find Lie symmetry, followed by conservation laws using ‘Multiplier’ approach. Finally, possibilities of associations between symmetry with conservation law will be used to reduce the differential equation, and thereby solve the differential equation. These methods will be used on some physically very important nonlinear differential equations; such as Kadomtsev- Petviashvili equation, Boyer-Finley equation, Short Pulse Equation, and Kortewegde Vries-Burgers equations. Furthermore, verification of the solution obtained also will be done by function of PDETest integrated in Maple or comparison to exist literature

Extractions of some new travelling wave solutions to the conformable Date-Jimbo-Kashiwara-Miwa equation

In this paper, complex and combined dark-bright characteristic properties of nonlinear Date-Jimbo-Kashiwara-Miwa equation with conformable are extracted by using two powerful analytical approaches. Many graphical representations such as 2D, 3D and contour are also reported. Finally, general conclusions of about the novel findings are introduced at the end of this manuscript

Exploring the Dynamics of Nonlocal Nonlinear Waves: Analytical Insights into the Extended Kadomtsev-Petviashvili Model

The study of nonlocal nonlinear systems and their dynamics is a rapidly increasing field of research. In this study, we take a closer look at the extended nonlocal Kadomtsev-Petviashvili (enKP) model through a systematic analysis of explicit solutions. Using a superposed bilinearization approach, we obtained a bilinear form of the enKP equation and constructed soliton solutions. Our findings show that the nature of the resulting nonlinear waves, including the amplitude, width, localization, and velocity, can be controlled by arbitrary solution parameters. The solutions exhibited both symmetric and asymmetric characteristics, including localized bell-type bright solitons, superposed kink-bell-type and antikink-bell-type soliton profiles. The solitons arising in this nonlocal model only undergo elastic interactions while maintaining their initial identities and shifting phases. Additionally, we demonstrated the possibility of generating bound-soliton molecules and breathers with appropriately chosen soliton parameters. The results of this study offer valuable insights into the dynamics of localized nonlinear waves in higher-dimensional nonlocal nonlinear models.Comment: 22 pages, 10 figures; submitted to journa