Symmetry and Painlevé analysis for the extended Sakovich equation

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Gangwei Wang ◽  
Abdul-Majid Wazwaz
Keyword(s):  
Lie Group ◽  
Design Methodology ◽  
Original Work ◽  
Soliton Solutions ◽  
Symmetry Analysis ◽  
Group Method ◽  
Invariant Solutions ◽  
Content Type ◽  
Lie Group Method ◽  
Practical Implications

Purpose The purpose of this paper is to concern with introducing symmetry analysis to the extended Sakovich equation. Design/methodology/approach The newly developed Sakovich equation has been handled by using the Lie symmetries via using the Lie group method. Findings The developed extended Sakovich model exhibit symmetries and invariant solutions. Research limitations/implications The present study is to address the two main motivations: the study of symmetry analysis and the study of soliton solutions of the extended Sakovich equation. Practical implications The work introduces symmetry analysis to the Painlevé-integrable extended Sakovich equation. Social implications The work presents useful symmetry algorithms for handling new integrable equations. Originality/value The paper presents an original work with symmetry analysis and shows useful findings.

Two new Painlevé-integrable extended Sakovich equations with (2 + 1) and (3 + 1) dimensions

2019 ◽  
Vol 30 (3) ◽  
pp. 1379-1387 ◽  
Author(s):  
Abdul-Majid Wazwaz
Keyword(s):  
Design Methodology ◽  
Original Work ◽  
Direct Method ◽  
Soliton Solutions ◽  
Complete Integrability ◽  
Integrable Equations ◽  
Content Type ◽  
Multiple Soliton Solutions ◽  
Multiple Complex Soliton Solutions ◽  
Practical Implications

Purpose The purpose of this paper is to introduce two new Painlevé-integrable extended Sakovich equations with (2 + 1) and (3 + 1) dimensions. The author obtains multiple soliton solutions and multiple complex soliton solutions for these three models. Design/methodology/approach The newly developed Sakovich equations have been handled by using the Hirota’s direct method. The author also uses the complex Hirota’s criteria for deriving multiple complex soliton solutions. Findings The developed extended Sakovich models exhibit complete integrability in analogy with the original Sakovich equation. Research limitations/implications This paper is to address these two main motivations: the study of the integrability features and solitons solutions for the developed methods. Practical implications This paper introduces two Painlevé-integrable extended Sakovich equations which give real and complex soliton solutions. Social implications This paper presents useful algorithms for constructing new integrable equations and for handling these equations. Originality/value This paper gives two Painlevé-integrable extended equations which belong to second-order PDEs. The two developed models do not contain the dispersion term uxxx. This paper presents an original work with newly developed integrable equations and shows useful findings.

Combating corruption in Nigeria and the constitutional issues arising

2016 ◽  
Vol 23 (4) ◽  
pp. 700-724 ◽  
Author(s):  
Akume T. Albert
Keyword(s):  
Analytical Method ◽  
Design Methodology ◽  
Original Work ◽  
Social Implications ◽  
Plea Bargain ◽  
Content Type ◽  
Documentary Sources ◽  
The Law ◽  
The Government ◽  
Practical Implications

Purpose The purpose of this paper therefore is to identify and examine major issue-areas in law, prominent among which are the Plea-Bargain and S308 Immunity Clause, and how they impact the process of effectively combating corruption in Nigeria. Design/methodology/approach The paper uses documentary sources and analytical method to examine the issues involved. Findings The identified issue-areas are inhibitors rather than facilitators. Research limitations/implications The implication is that the government needs to change the existing laws to strengthen the fight against corruption. Practical implications This is to ensure that the war against corruption is strengthened and effective. Social implications To ensure that offenders face the full weight of the law for their action. Originality/value This paper is the author's original work and all references are appropriately acknowledged.

Symmetry reductions and rational non-traveling wave solutions for the (2+1)-D Ablowitz-Kaup-Newell-Segur equation

2016 ◽  
Vol 26 (8) ◽  
pp. 2331-2339 ◽  
Author(s):  
Xiao-rong Kang ◽  
Xian Daquan
Keyword(s):  
Lie Group ◽  
Traveling Wave ◽  
Function Method ◽  
Traveling Wave Solutions ◽  
Group Method ◽  
Content Type ◽  
Lie Group Method ◽  
Localized Structures ◽  
Wave Solutions ◽  
Akns Equation

Purpose 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. Design/methodology/approach Along with some special transformations, the Lie group method and the rational function method are applied to the (2+1)-dimensional AKNS equation. Findings Some new non-traveling wave solutions are obtained, including generalized rational solutions with two arbitrary functions of time variable. Research limitations/implications As a typical nonlinear evolution equation, some dynamical behaviors are also discussed. Originality/value 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.

Colour, culture and difference in Australian teacher education: voices from the edge

2019 ◽  
Vol 19 (3) ◽  
pp. 324-343
Author(s):  
Dawn Joseph ◽  
Richard Johnson
Keyword(s):  
Lived Experience ◽  
Design Methodology ◽  
Original Work ◽  
Minority Groups ◽  
Staff Perceptions ◽  
Content Type ◽  
Academic Communities ◽  
The Social ◽  
Metropolitan Universities ◽  
Practical Implications

Purpose Although much has been written about international students in higher education in Australia, there is a paucity of research and discussion about international academics especially non-whites and their lived experience in the workplace. This paper represents the voices of two academics working in metropolitan universities in Melbourne. The purpose of this paper is to raise awareness of how in spite of all the goodwill and highbrow research, the “corridors of academia” need to be examined in considering the politics of inclusion and internationalisation as the authors still need to address issues of colour as they exist in the academy. Design/methodology/approach The authors use narrative inquiry and reflection to tell the story as both phenomenon and method where the phenomenon is the story and inquiry is the narrative. Findings The findings suggest student and staff perceptions of difference are mostly theorised but not practiced within the academy. Research limitations/implications The paper includes two voices, a limitation in itself, thus generalisations cannot be made to other academics or institutions. The authors recommend more professional development for staff and students alike to embrace issues of colour, culture and difference. Practical implications The authors draw attention to the need for academics to reflect on their behaviour within their own academic communities and be more aware of minority groups in academia. Social implications By including and listening to issues facing minority groups (academics and students) can only improve the social cohesion of university worksites. Originality/value This is an original work carried out by both authors. It raises concerns that may also be experienced international staff and or students.

scholarly journals Lie symmetry analysis and conservation law for the equation arising from higher order Broer-Kaup equation

2019 ◽  
Vol 17 (1) ◽  
pp. 1045-1054
Author(s):  
Hengtai Wang ◽  
Huiwen Chen ◽  
Zigen Ouyang ◽  
Fubin Li
Keyword(s):  
Lie Group ◽  
Conservation Law ◽  
Higher Order ◽  
Lie Symmetry ◽  
Symmetry Analysis ◽  
Optimal System ◽  
Group Method ◽  
Lie Symmetry Analysis ◽  
Lie Group Method ◽  
Similarity Reductions

Abstract In this paper, Lie symmetry analysis is performed for the equation derived from $(2+1)$-dimensional higher order Broer-Kaup equation. Meanwhile, the optimal system and similarity reductions based on the Lie group method are obtained. Furthermore, the conservation law is studied via the Ibragimov’s method.

scholarly journals Symmetry analysis of a (2+1)-D system

2018 ◽  
Vol 22 (4) ◽  
pp. 1811-1822
Author(s):  
Yan Wang ◽  
Zhong-Zhou Dong
Keyword(s):  
Lie Group ◽  
Symmetry Analysis ◽  
Vector Analysis ◽  
Group Method ◽  
Lie Group Method ◽  
Generalized Symmetry ◽  
Symmetry Method ◽  
Burgers System

The classical Lie group method and the (2+1)-D generalized symmetry method in vector analysis are adopted to find infinitesimal symmetries for a (2+1)-D generalized Painleve Burgers system, and its various reduced systems are obtained.

Painlevé analysis for new (3 + 1)-dimensional Boiti–Leon–Manna–Pempinelli equations with constant and time-dependent coefficients

2019 ◽  
Vol 30 (9) ◽  
pp. 4259-4266 ◽  
Author(s):  
Abdul-Majid Wazwaz
Keyword(s):  
Design Methodology ◽  
Soliton Solutions ◽  
Time Dependent ◽  
Integrable Equations ◽  
Content Type ◽  
Multiple Soliton Solutions ◽  
Simplified Hirota’S Method ◽  
Constant Coefficients ◽  
Multiple Complex Soliton Solutions ◽  
Practical Implications

Purpose The purpose of this paper is to introduce two new (3 + 1)-dimensional Boiti–Leon–Manna–Pempinelli (BLMP) equations, the first with constant coefficients and the other with time-dependent coefficients. The author obtains multiple soliton solutions and multiple complex soliton solutions for the two developed models. Design/methodology/approach The newly developed models with constant coefficients and with time-dependent coefficients have been handled by using the simplified Hirota’s method. The author also uses the complex Hirota’s criteria for deriving multiple complex soliton solutions. Findings The two developed BLMP models exhibit complete integrability for any constant coefficient and any analytic time-dependent coefficients by investigating the compatibility conditions for each developed model. Research limitations/implications The paper presents an efficient algorithm for handling integrable equations with constant and analytic time-dependent coefficients. Practical implications The paper presents two new integrable equations with a variety of coefficients. The author showed that integrable equations with constant and time-dependent coefficients give real and complex soliton solutions. Social implications The paper presents useful algorithms for finding and studying integrable equations with constant and time-dependent coefficients. Originality/value The paper presents an original work with a variety of useful findings.

Training for enabling environments

2017 ◽  
Vol 38 (1) ◽  
pp. 41-48
Author(s):  
Aldo Lombardo ◽  
Rex Haigh
Keyword(s):  
Quality Improvement ◽  
Design Methodology ◽  
Original Work ◽  
Learning Experience ◽  
Psychological Impact ◽  
Training Experience ◽  
Direct Experience ◽  
Content Type ◽  
Written Explanations ◽  
Practical Implications

Purpose The purpose of this paper is to demonstrate the training value of a residential “enabling environments” (LLEE) workshop in relation to the Royal College of Psychiatrists’ (RCPsych) ten specified standards, as rated by workshop participants. Design/methodology/approach A 34 question yes/no/na questionnaire was drawn up, derived from the ten value-based standards and criteria which need to be met for the enabling environment (EE) award by the RCPsych’s Centre for Quality Improvement (Table AI). It was administered after six residential workshops, in Italy and UK, to 99 participants. Results were analysed for each of the six workshops, and for each of the ten standards, to show the degree to which participants recognised whether the standards were met. Findings High rates of positive responses were recorded with little variation across the six workshops sampled. Some standards and criteria showed higher levels of positive responses, and some showed slightly higher scores for “not applicable”. Practical implications Experiential Living-Learning Experience (LLE) workshops provide a valid training experience for those developing or working in EEs. Social implications Value-based standards can only be fully understood by direct experience of them, as verbal or written explanations fail to convey the psychological impact of the experience. Originality/value The questionnaire and its translation is the original work of AL. RH is the founder of LLE training workshops and the EE award.

A new (3 + 1)-dimensional Painlevé-integrable Sakovich equation: multiple soliton solutions

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Abdul-Majid Wazwaz
Keyword(s):  
Design Methodology ◽  
Soliton Solutions ◽  
Complete Integrability ◽  
Content Type ◽  
Hirota’S Method ◽  
Multiple Soliton Solutions ◽  
Simplified Hirota’S Method ◽  
Hirota's Method ◽  
Practical Implications ◽  
Dispersion Term

Purpose This paper aims to develop a new (3 + 1)-dimensional Painlev´e-integrable extended Sakovich equation. This paper formally derives multiple soliton solutions for this developed model. Design/methodology/approach This paper uses the simplified Hirota’s method for deriving multiple soliton solutions. Findings This paper finds that the developed (3 + 1)-dimensional Sakovich model exhibits complete integrability in analogy with the standard Sakovich equation. Research limitations/implications This paper addresses the integrability features of this model via using the Painlev´e analysis. This paper reports multiple soliton solutions for this equation by using the simplified Hirota’s method. Practical implications The study reports three non-linear terms added to the standard Sakovich equation. Social implications The study presents useful algorithms for constructing new integrable equations and for handling these equations. Originality/value The paper reports a new Painlev´e-integrable extended Sakovich equation, which belongs to second-order partial differential equations. The constructed model does not contain any dispersion term such as uxxx.

Defining and measuring the productive office

2019 ◽  
Vol 21 (1) ◽  
pp. 55-71 ◽  
Author(s):  
Rob Harris
Keyword(s):  
Literature Review ◽  
Built Environment ◽  
Design Methodology ◽  
Research Team ◽  
Original Work ◽  
Content Type ◽  
Office Environment ◽  
British Council ◽  
Practical Implications

Purpose This paper aims to provide a perspective on the office productivity debate, with a particular focus on providing a framework for examining those factors relating to the design and management of the office environment. Design/methodology/approach The approach taken has been to examine the plethora of factors that might be involved, principally through a literature review, and then to group these into four generic areas of enquiry. Within each of these, potential measures of productivity are described, and these are connected to building lifecycle decisions. Findings Combined, the findings produce a practical framework within which various actors in the design, delivery and management offices can understand and influence the productivity question. In this way, the findings have practical implications rather than simply describing the factors that influence productivity. Originality/value The paper develops a report produced in 2017 for the British Council for Offices. Building on the main findings of the original work, this paper expands the literature review, provides more context regarding the significance of office productivity and expands upon the conclusions. The author fully acknowledges the contributions of the whole research team behind the original paper. The originality of the work lies in its development of a framework that can be applied by practitioners in the built environment.

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