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The purpose of this paper is to find new non-traveling wave solutions and study its localized structure of Caudrey-Dodd-Gibbon-Kotera-Sawada (CDGKS) equation.

The authors apply the Lie group method twice and combine with the Exp-function method and Riccati equation mapping method to the (2+1)-dimensional CDGKS equation.

The authors have obtained some new non-traveling wave solutions with two arbitrary functions of time variable.

As non-linear evolution equations is characterized by rich dynamical behavior, the authors just found some of them and others still to be found.

These results may help the authors to investigate some new localized structure and the interaction of waves in high-dimensional models. The new non-traveling wave solutions with two arbitrary functions of time variable are obtained for CDGKS equation using Lie group approach twice and combining with the Exp-function method and Riccati equation mapping method by the aid of Maple.

The purpose of this paper is to find out some new rational non-traveling wave solutions and to study localized structures for (2+1)-dimensional Ablowitz-Kaup-Newell-Segur (AKNS) equation.

Along with some special transformations, the Lie group method and the rational function method are applied to the (2+1)-dimensional AKNS equation.

Some new non-traveling wave solutions are obtained, including generalized rational solutions with two arbitrary functions of time variable.

As a typical nonlinear evolution equation, some dynamical behaviors are also discussed.

With the help of the Lie group method, special transformations and the rational function method, new non-traveling wave solutions are derived for the AKNS equation by Maple software. These results are much useful for investigating some new localized structures and the interaction of waves in high-dimensional models, and enrich dynamical features of solutions for the higher dimensional systems.

The purpose of this paper is to discuss the homoclinic breathe-wave solutions and the singular periodic solutions for (2 + 1)-dimensional generalized shallow water wave (GSWW) equation.

The Hirota bilinear method, the Lie symmetry method and the non-Lie symmetry method are applied to the (2 + 1)D GSWW equation.

A reduced (1 + 1)D potential KdV equation can be derived, and its soliton solutions are also presented.

As a typical nonlinear evolution equation, some dynamical behaviors are also discussed.

These results are very useful for investigating some localized geometry structures of dynamical behaviors and enriching dynamical features of solutions for the higher dimensional systems.

The purpose of this paper is to find the exact solutions of a (3 + 1)-dimensional non-integrable Korteweg-de Vries type (KdV-type) equation, which can be used to describe the stability of soliton in a nonlinear media with weak dispersion.

The authors apply the extended Bell polynomial approach, Hirota’s bilinear method and the homoclinic test technique to find the rogue waves, homoclinic breather waves and soliton waves of the (3 + 1)-dimensional non-integrable KdV-type equation. The used approach formally derives the essential conditions for these solutions to exist.

The results show that the equation exists rogue waves, homoclinic breather waves and soliton waves. To better understand the dynamic behavior of these solutions, the authors analyze the propagation and interaction properties of the these solutions.

These results may help to investigate the local structure and the interaction of waves in KdV-type equations. It is hoped that the results can help enrich the dynamic behavior of such equations.

The purpose of this paper is to study the homoclinic breather waves, rogue waves and multi-soliton waves of the (2 + 1)-dimensional Mel’nikov equation, which describes an interaction of long waves with short wave packets.

The author applies the Hirota’s bilinear method, extended homoclinic test approach and parameter limit method to construct the homoclinic breather waves and rogue waves of the (2 + 1)-dimensional Mel’nikov equation. Moreover, multi-soliton waves are constructed by using the three-wave method.

The results imply that the (2 + 1)-dimensional Mel’nikov equation has breather waves, rogue waves and multi-soliton waves. Moreover, the dynamic properties of such solutions are displayed vividly by figures.

This paper presents efficient methods to find breather waves, rogue waves and multi-soliton waves for nonlinear evolution equations.

The outcome suggests that the extreme behavior of the homoclinic breather waves yields the rogue waves. Moreover, the multi-soliton waves are constructed, including the new breather two-solitary and two-soliton solutions. Meanwhile, the dynamics of these solutions will greatly enrich the diversity of the dynamics of the (2 + 1)-dimensional Mel’nikov equation.

Underpinned by sensation-seeking theory (SST) and regulatory focus theory (RFT), this paper highlights the crucial role of adventurousness in self-protective behavior and future travel avoidance. Furthermore, this paper investigates safety-seeking tendency as a moderator and travel anxiety post-COVID-19 as a mediator.

Data were gathered from 574 potential visitors to St. Catherine post-COVID-19 and analyzed using Smart-PLS approach.

Adventurousness negatively and significantly affected travel anxiety, while the latter negatively influenced self-protective behavior and positively influenced future travel avoidance. Besides, the findings proved that travel anxiety partially mediated the adventurousness linkage with self-protective behavior and future travel avoidance. Moreover, safety-seeking tendencies dampened travel anxiety's connection with self-protective behavior and future travel avoidance.

This paper provides valuable insights into travel research in theory and practice to revive tourist attractions post-COVID-19 in developing countries via an adventure tourism pattern. The study helps figure out how to deal with the pandemic and restore the monument of heavenly religions, St. Catherine—sacred mountain peaks, mosques, churches and many monasteries—in addition to its charming and picturesque nature.

The current paper examines a traveler's adventurous nature and post-COVID-19 behavior when visiting St. Catherine and their behaviors related to future avoidance and self-protection. This paper adds the first investigation of travel anxiety and safety-seeking through the lens of SST and RFT theories in the Egyptian tourism context.

The traditional means of procuring airline tickets and associate travel arrangements are rapidly changing. The advent and proliferation of computers, coupled with the increasingly acceptable leveraging of the Internet has caused some major changes in the travel industry. These changes are primarily being facilitated by Internet travel marketplaces (such as Expedia, Orbitz, and Travelvelocity) that claim to provide an easier, less expensive alternative to traditional methods of ticket procurement without sacrificing service quality. If travel marketplaces are to be successful then they need to understand their customers and what the motivations behind their actions when it comes to shopping for discount travel. However, there are required information exchanges on the part of both the service provider and the consumer that are not without perceived risks and required a sense of mutual trust. This paper looked at online consumer behavior as it pertains to e‐travel through the theoretical perspectives of expectancy theory and the technical acceptance model by inspecting selected motives and experiences of the consumer and specifically what these Web sites offer.

The purpose of this paper is to propose a social semiotic approach to analysing objects of learning in terms of their critical aspects.

The design for this paper focuses on how the semiotic resources – including language, equations, and diagrams – that are commonly used in physics teaching realise the critical aspects of a common physics object of learning. A social semiotic approach to the analysis of a canonical text extract from optics is presented to illustrate how critical aspects can be identified.

Implications for university teaching and learning of physics stemming from this social semiotic approach are suggested.

Hitherto under-explored similarities between the Variation Theory of Learning, which underpins learning studies, and a social semiotic approach to meaning-making are identified. These similarities are used to propose a new, potentially very powerful approach to identifying critical aspects of objects of learning.