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The purpose of this study is to investigate the nonlinear Schrödinger equation (NLS) incorporating spatiotemporal dispersion and other dispersive effects. The goal is to derive various soliton solutions, including bright, dark, singular, periodic and exponential solitons, to enhance the understanding of soliton propagation dynamics in nonlinear metamaterials (MMs) and contribute new findings to the field of nonlinear optics.

The research uses a range of powerful mathematical approaches to solve the NLS. The proposed methodologies are applied systematically to derive a variety of optical soliton solutions, each demonstrating unique optical behaviors and characteristics. The approach ensures that both the theoretical framework and practical implications of the solutions are thoroughly explored.

The study successfully derives several types of soliton solutions using the aforementioned mathematical approaches. Key findings include bright optical envelope solitons, dark optical envelope solitons, periodic solutions, singular solutions and exponential solutions. These results offer new insights into the behavior of ultrashort solitons in nonlinear MMs, potentially aiding further research and applications in nonlinear wave studies.

This study makes an original contribution to nonlinear optics by deriving new soliton solutions for the NLS with spatiotemporal dispersion. The diversity of solutions, including bright, dark, periodic, singular and exponential solitons, adds substantial value to the existing body of knowledge. The use of distinct and reliable methodologies to obtain these solutions underscores the novelty and potential applications of the research in advancing optical technologies. The originality lies in the novel approaches used to obtain these diverse soliton solutions and their potential impact on the study and application of nonlinear waves in MMs.

After studying and analyzing this case, students will be able to evaluate the strategic alternatives for growth for a small entrepreneurial business in an emerging market, analyze the trade-offs between maintaining continuity and change in the growth strategy adopted by an organization and synthesize an appropriate growth strategy for managing the trade-off between continuity and change in an organization.

It was late April 2022, and Mohammad Hamza – the founder and marketing head of Engineering & Environmental Solutions (E&E Solutions) – disconnected the call of his sales manager. His mind was fixated on how to craft the strategy for the next phase of the company’s growth. The deadline for their biggest tender was at the end of May 2022. Should he commit all the company’s reserves to this project or pursue global markets? Launched in 2015, E&E Solutions had come a long way from being a start-up with just one product to a full-blown manufacturer and environmental monitoring equipment service provider. Growing pollution and strictness in compliance propelled the demand for environmental monitoring equipment in India, poised to reach $342m by 2025. E&E Solutions leveraged its technological capabilities in Internet of Things and sensors producing low-cost monitoring equipment to gain an edge in an evolving market and bootstrapped its way to almost $5m annual turnover in 2021. However, the last review meeting brought many concerns for the next growth phase. E&E Solutions had so far focused on the domestic market, catering to the demands of private as well as government clients. A significant cause for concern had been the small order size of private players, averaging $2,000 and a lower net margin of 8%. Moreover, the company had been missing out on opportunities to bid for large government contracts owing to stringent bidding credentials required (such as turnover of at least 50%–80% of the project value and previous similar order experience with a range of at least 70% of the project value). Furthermore, the COVID-19 pandemic had stalled their efforts to tap a promising global environmental monitoring market (predicted to be $44bn by 2030). As Hamza and his team sat in their board room for a discussion, they had two alternatives. Either continue focusing on the domestic market, especially the big government contracts (more than $12m order size) or explore the markets in other emerging economies with demand for similar products (such as Middle East and North Africa region) more aggressively. Hamza was, however, wondering if they could do both, for he knew that to qualify for big government contracts, they needed to scale up. He was also getting restless after missing his target of reaching $20m in five years, especially since India’s ecosystem for start-ups and the small business sector had witnessed favorable policies and support from the government. He started pondering how to leverage his organization’s strengths and continuities to achieve the required pace and scale of change. His thoughts wandered around dividing the cash reserves of $500,000 to fuel growth without reducing the R&D budget. After all, R&D has been E&E Solutions’ forte since its inception and has been pivotal in creating its differentiation.

This case study can be used for core strategic management course at the undergraduate and graduate level of management programs. It can also be used in advanced strategy courses like strategic change, entrepreneurship and small business management offered in MBA programs.

Teaching notes are available for educators only.

CSS 11: Strategy

This study aims to identify European positioning on the use of remote customer onboarding solutions in combating financial crime.

This study is a desktop research that examines European Banking Authority (EBA) policy statements relating to the use of innovative solutions in combating financial crime.

Technological advancements in biometric data and software tools provide a unique opportunity to address potential paper customer onboarding process deficiencies. Electronic remote customer onboarding solutions equip credit, financial institutions and investment firms with an alternative FTE cost-saving solution, in their pursuit of revenue generation. Whilst the EBA and Financial Action Task Force have provided approval for the utilisation of innovative solutions and AML technologies in combatting financial crime. Hesitancy remains on the ability of credit and financial institutions to use technological solutions as a “magic solution” in preventing the materialisation of money laundering/terrorist financing related risks. Analysis of policy suggests a gravitation towards the increased use of the aforementioned technologies in the interim.

Capitalisation of European banking authority.

The paper aims to study the constraint solutions of the periodic coupled operator matrix equations by the biconjugate residual algorithm. The new algorithm can solve a lot of constraint solutions including Hamiltonian solutions and symmetric solutions, as special cases. At the end of this paper, the new algorithm is applied to the pole assignment problem.

When the studied periodic coupled operator matrix equations are consistent, it is proved that constraint solutions can converge to exact solutions. It is demonstrated that the solutions of the equations can be obtained by the new algorithm with any arbitrary initial matrices without rounding error in a finite number of iterative steps. In addition, the least norm-constrained solutions can also be calculated by selecting any initial matrices when the equations of the periodic coupled operator matrix are inconsistent.

Numerical examples show that compared with some existing algorithms, the proposed method has higher convergence efficiency because less data are used in each iteration and the data is sufficient to complete an update. It not only has the best convergence accuracy but also requires the least running time for iteration, which greatly saves memory space.

Compared with previous algorithms, the main feature of this algorithm is that it can synthesize these equations together to get a coupled operator matrix equation. Although the equation of this paper contains multiple submatrix equations, the algorithm in this paper only needs to use the information of one submatrix equation in the equation of this paper in each iteration so that different constraint solutions of different (coupled) matrix equations can be studied for this class of equations. However, previous articles need to iterate on a specific constraint solution of a matrix equation separately.

This study aims to explore a novel model that integrates the Kairat-II equation and Kairat-X equation (K-XE), denoted as the Kairat-II-X (K-II-X) equation. This model demonstrates the connections between the differential geometry of curves and the concept of equivalence.

The Painlevé analysis shows that the combined K-II-X equation retains the complete Painlevé integrability.

This study explores multiple soliton (solutions in the form of kink solutions with entirely new dispersion relations and phase shifts.

Hirota’s bilinear technique is used to provide these novel solutions.

This study also provides a diverse range of solutions for the K-II-X equation, including kink, periodic and singular solutions.

This study provides formal procedures for analyzing recently developed systems that investigate optical communications, plasma physics, oceans and seas, fluid mechanics and the differential geometry of curves, among other topics.

The study introduces a novel Painlevé integrable model that has been constructed and delivers valuable discoveries.

The boundary integral method (BIM) is very attractive to practicing engineers as it reduces the dimensionality of the problem by one, thereby making the procedure computationally inexpensive compared to its peers. The principal feature of this technique is the limitation of all its computations to only the boundaries of the domain. Although the procedure is well developed for the Laplace equation, the Poisson equation offers some computational challenges. Nevertheless, the literature provides a couple of solution methods. This paper revisits an alternate approach that has not gained much traction within the community. The purpose of this paper is to address the main bottleneck of that approach in an effort to popularize it and critically evaluate the errors introduced into the solution by that method.

The primary intent in the paper is to work on the particular solution of the Poisson equation by representing the source term through a Fourier series. The evaluation of the Fourier coefficients requires a rectangular domain even though the original domain can be of any arbitrary shape. The boundary conditions for the homogeneous solution gets modified by the projection of the particular solution on the original boundaries. The paper also develops a new Gauss quadrature procedure to compute the integrals appearing in the Fourier coefficients in case they cannot be analytically evaluated.

The current endeavor has developed two different representations of the source terms. A comprehensive set of benchmark exercises has successfully demonstrated the effectiveness of both the methods, especially the second one. A subsequent detailed analysis has identified the errors emanating from an inadequate number of boundary nodes and Fourier modes, a high difference in sizes between the particular solution and the original domains and the used Gauss quadrature integration procedures. Adequate mitigation procedures were successful in suppressing each of the above errors and in improving the solution accuracy to any desired level. A comparative study with the finite difference method revealed that the BIM was as accurate as the FDM but was computationally more efficient for problems of real-life scale. A later exercise minutely analyzed the heat transfer physics for a fin after validating the simulation results with the analytical solution that was separately derived. The final set of simulations demonstrated the applicability of the method to complicated geometries.

First, the newly developed Gauss quadrature integration procedure can efficiently compute the integrals during evaluation of the Fourier coefficients; the current literature lacks such a tool, thereby deterring researchers to adopt this category of methods. Second, to the best of the author’s knowledge, such a comprehensive error analysis of the solution method within the BIM framework for the Poisson equation does not currently exist in the literature. This particular exercise should go a long way in increasing the confidence of the research community to venture into this category of methods for the solution of the Poisson equation.

The purpose of the article is to conduct a mathematical and theoretical analysis of soliton solutions for a specific nonlinear evolution equation known as the (2 + 1)-dimensional Zoomeron equation. Solitons are solitary wave solutions that maintain their shape and propagate without changing form in certain nonlinear wave equations. The Zoomeron equation appears to be a special model in this context and is associated with other types of solitons, such as Boomeron and Trappon solitons. In this work, the authors employ two mathematical methods, the modified F-expansion approach with the Riccati equation and the modified generalized Kudryashov’s methods, to derive various types of soliton solutions. These solutions include kink solitons, dark solitons, bright solitons, singular solitons, periodic singular solitons and rational solitons. The authors also present these solutions in different dimensions, including two-dimensional, three-dimensional and contour graphics, which can help visualize and understand the behavior of these solitons in the context of the Zoomeron equation. The primary goal of this article is to contribute to the understanding of soliton solutions in the context of the (2 + 1)-dimensional Zoomeron equation, and it serves as a mathematical and theoretical exploration of the properties and characteristics of these solitons in this specific nonlinear wave equation.

The article’s methodology involves applying specialized mathematical techniques to analyze and derive soliton solutions for the (2 + 1)-dimensional Zoomeron equation and then presenting these solutions graphically. The overall goal is to contribute to the understanding of soliton behavior in this specific nonlinear equation and potentially uncover new insights or applications of these soliton solutions.

As for the findings of the article, they can be summarized as follows: The article provides a systematic exploration of the (2 + 1)-dimensional Zoomeron equation and its soliton solutions, which include different types of solitons. The key findings of the article are likely to include the derivation of exact mathematical expressions that describe these solitons and the successful visualization of these solutions. These findings contribute to a better understanding of solitons in this specific nonlinear wave equation, potentially shedding light on their behavior and applications within the context of the Zoomeron equation.

The originality of this article is rooted in its exploration of soliton solutions within the (2 + 1)-dimensional Zoomeron equation, its application of specialized mathematical methods and its successful presentation of various soliton types through graphical representations. This research adds to the understanding of solitons in this specific nonlinear equation and potentially offers new insights and applications in this field.

The purpose of this study is to produce families of exact soliton solutions (2+1)-dimensional Korteweg-de Vries (KdV) equation, that describes shallow water waves, using an ansätze approach.

This article aims to introduce a recently developed ansätze for creating soliton and travelling wave solutions to nonlinear nonintegrable partial differential equations, especially those with physical significance.

A recently developed ansätze solution was used to successfully construct soliton solutions to the (2 + 1)-dimensional KdV equation. This straightforward method is an alternative to the Painleve test analysis, yielding similar results. The strategy demonstrated the existence of a single soliton solution, also known as a localized wave or bright soliton, as well as singular solutions or kink solitons.

The ansätze solution used to construct soliton solutions to the (2 + 1)-dimensional KdV equation is novel. New soliton solutions were also obtained.

Reports findings from a major study done by a Boston consulting firm showing four solution‐based market segments in high‐tech industries. They are the specialized solution, the customized solution, the value solution, and the packaged solution. One segment is the be‐first “contrarian” buyer. One segment responds to aggressive selling while another reacts to market pull. And the fourth segment is retail‐oriented. This article may be useful to both buyers and sellers of technology in emerging, unsaturated markets.

Presents findings from a study of the effects of treating unbleached bagasse paper sheets with different resin solutions. Unbleached kraft bagasse paper sheets were treated with different resin solutions such as nitrocellulose, melamine formaldehyde, silicone, short and medium alkyd resin and the physico‐mechanical properties of the modified paper sheets were tested. The strength properties of treated paper sheets were highly improved especially in the case of treatment with melamine formaldehyde and silicone resin solutions. The effect of dipping time of paper sheets in different concentrations of resin solution on the strength properties was also investigated. Physico‐mechanical properties of thermally treated modified paper sheets with resins were also clarified. Concludes that promising results in the improvement of insulation of treated paper sheets with resin are obtained by studying the dielectric‐electric properties.