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 solitons, such as 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.

In this article, we investigate the propagation of acceleration waves in a perfectly conducting, inviscid gas subjected to an oblique magnetic field. The reference coordinate system used to study the transmission of acceleration waves along characteristic paths is constructed based on the eigenvalues of the quasilinear hyperbolic system of equations. A transport equation is derived to examine the growth and decay behavior of the acceleration waves. Special attention is given to analyzing the influence of magnetic field components on shock wave formation in both planar and cylindrically symmetric flows. Furthermore, it is demonstrated that a linear solution of the governing system of equations in the characteristic plane exhibits nonlinear behavior in the physical plane.