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This study aims to investigate two newly developed (3 + 1)-dimensional Kairat-II and Kairat-X equations that illustrate relations with the differential geometry of curves and equivalence aspects.

The Painlevé analysis confirms the complete integrability of both Kairat-II and Kairat-X equations.

This study explores multiple soliton solutions for the two examined models. Moreover, the author showed that only Kairat-X give lump solutions and breather wave solutions.

The Hirota’s bilinear algorithm is used to furnish a variety of solitonic solutions with useful physical structures.

This study also furnishes a variety of numerous periodic solutions, kink solutions and singular solutions for Kairat-II equation. In addition, lump solutions and breather wave solutions were achieved from Kairat-X model.

The work formally furnishes algorithms for studying newly constructed systems that examine plasma physics, optical communications, oceans and seas and the differential geometry of curves, among others.

This paper presents an original work that presents two newly developed Painlev\'{e} integrable models with insightful findings.

The purpose of this study is to solve two unique but difficult partial differential equations: the foam drainage equation and the nonlinear time-fractional fisher’s equation. Through our methods, we aim to provide accurate solutions and gain a deeper understanding of the intricate behaviors exhibited by these systems.

In this study, we use a dual technique that combines the Aboodh residual power series method and the Aboodh transform iteration method, both of which are combined with the Caputo operator.

We develop exact and efficient solutions by merging these unique methodologies. Our results, presented through illustrative figures and data, demonstrate the efficacy and versatility of the Aboodh methods in tackling such complex mathematical models.

Owing to their fractional derivatives and nonlinear behavior, these equations are crucial in modeling complex processes and confront analytical complications in various scientific and engineering contexts.

This paper is devoted to the generalized Kadomtsev–Petviashvili I equation. This study aims to propose a new approach for investigation for the existence of at least one global classical solution and the existence of at least two nonnegative global classical solutions. The main arguments in this paper are based on some recent theoretical results.

This paper is devoted to the generalized Kadomtsev–Petviashvili I equation. This study aims to propose a new approach for investigation for the existence of at least one global classical solution and the existence of at least two nonnegative global classical solutions. The main arguments in this paper are based on some recent theoretical results.

This paper is devoted to the generalized Kadomtsev–Petviashvili I equation. This study aims to propose a new approach for investigation for the existence of at least one global classical solution and the existence of at least two nonnegative global classical solutions. The main arguments in this paper are based on some recent theoretical results.

This article is devoted to the generalized Kadomtsev–Petviashvili I equation. This study aims to propose a new approach for investigation for the existence of at least one global classical solution and the existence of at least two nonnegative global classical solutions. The main arguments in this paper are based on some recent theoretical results.

The current study aims to empirically analyze the influence of different information sources, together with the persuasiveness of recommender systems (RSs) on the consumer’s purchase intention (PI). It also expands the research on RSs from the point of view of consumer behavior and psychology, considering perceived usefulness and relevance. In addition, it analyzes how different types of personalized recommendations, along with non-personalized ones, influence PI.

The proposed model has been validated using partial least squares structural equation modeling (PLS-SEM), based on the data collected from 597 online shoppers.

This study proves that both information search and RSs influence PI, being complementary rather than mutually exclusive. Recommender systems’ findings indicate that the PI is primarily influenced by the perceived relevance of RSs, the information provided by manufacturers and reviews. Moreover, only the influence of the perceived usefulness of personalized recommendations strongly affects PI. Conversely, non-personalized recommendations do not affect PI.

Developers should focus on increasing the perceived usefulness and relevance of RSs. Thus, they could adopt the hybridization of RSs with the aggregation of both personal shopping behavior and social network contacts. It should integrate information signals from multiple sources to include sentiment extracted from reviews or links to the manufacturer’s page. Furthermore, the recommendation of discounted products must be only for products preferred by customers, because only these influence the PI.

This research provides a structural model that examines together, for the first time, the influence on the PI of the main RSs and sources of information.