This study endeavors to examine the dynamics of the generalized Kadomtsev-Petviashvili (gKP) equation in (n + 1) dimensions. Based on the comprehensive three-wave methodology and the Hirota’s bilinear technique, the gKP equation is meticulously examined. By means of symbolic computation, a number of three-wave solutions are derived. Applying the Lie symmetry approach to the governing equation enables the determination of symmetry reduction, which aids in the reduction of the dimensionality of the said equation. Using symmetry reduction, we obtain the second order differential equation. By means of applying symmetry reduction, the second order differential equation is derived. The second order differential equation undergoes Galilean transformation to obtain a system of first order differential equations. The present study presents an analysis of bifurcation and sensitivity for a given dynamical system. Additionally, when an external force impacts the underlying dynamic system, its behavior resembles quasi-periodic phenomena. The presence of quasi-periodic patterns are identified using chaos detecting tools. These findings represent a novel contribution to the studied equation and significantly advance our understanding of dynamics in nonlinear wave models.

In this paper, we set up an adequate condition for the presence of a solution of the nonlinear matrix equation. To do so, we prove the existence of fixed points for multi-valued modified F-contractions in the context of complete metric spaces, which generalize, refine, and extend several existing results in the literature. An example is accompanies the obtained results to show that derived results are a proper generalization.

The thermophoretic motion (TM) system with a variable heat transmission factor, based on the Korteweg-de Vries (KdV) equation, is used to model soliton-like thermophoresis of creases in graphene sheets. Painlevé test is employed to discover that the equation is Painlevé integrable. Then an auto-Bäcklund transformation using the truncated Painlevé expansion is obtained. Concerning the additional variables, the auto-Bäcklund transformations convert the nonlinear model to a set of linear partial differential equations. Finally, various explicit precise solutions based on the acquired auto-Bäcklund transformations are investigated and the researched solutions are illustrated in 3D, 2D and contour plots. Furthermore, the Cole-Hopf transformation is used in conjunction with Hirota’s bilinear technique to get multiple regular and singular kink solutions.

In the context of complete strong $b$-metric-like spaces, we prove new multi-fixed point solutions for the pair of multivalued, dominated operators that fulfill the generalized nonlinear contractions on a closed ball. We employ a mix of two different types of mappings in our approach: one is a class of multi-dominated mappings, while the other is a weaker class of strictly increasing mappings. Additionally, some new fixed-point results concerning the multi-graph-dominated structure in graph contraction are presented. To validate the hypothesis of acquired results, a few sample cases are presented. A numerical experiment has been carried out to approximate the fixed point. In addition, to demonstrate the originality of our findings, we proposed simple and efficient solutions to the system of fractional differential equations and nonlinear Volterra-type integral equations.

In this manuscript, the Landau-Ginzburg-Higgs (LGH) equation is considered as an investigating model. To extract novel results from the governing equation, the $ G'/(b G'+G+a) $-expansion approach has been employed. Utilizing this approach, the outcomes are attained as hyperbolic and trigonometric functions. Kink, periodic and singular soliton solutions have been recovered by selecting the appropriate values for the parameters. The obtained findings for the LGH equation are displayed in 3-D, contour and 2-D profiles. Using Galilean transformation, the model is converted into a planar dynamical system, and qualitative analysis is investigated. Moreover, chaotic and quasi-periodic patterns have been addressed after including the perturbed term. Simulated results reveal that by modifying amplitude and frequency parameters, the dynamic behavior of the system can also be changed. The recorded results are novel and show the effectiveness and feasibility of the suggested technique for assessing soliton solutions and phase visualizations for different nonlinear models.

In this study, we prove the existence and uniqueness of a best proximity point in the setting of non-Archimedean modular metric spaces via the concept of simulation functions. A non-Archimedean metric modular is shaped as a parameterized family of classical metrics; therefore, for each value of the parameter, the positivity, the symmetry, the triangle inequality, or the continuity is ensured. Also, we demonstrate how analogous theorems in modular metric spaces may be used to generate the best proximity point results in triangular fuzzy metric spaces. The utility of our findings is further demonstrated by certain examples, illustrated consequences, and an application to fuzzy fractional differential equations.