New integrable Vakhnenko–Parkes (VP) equations with time-dependent coefficients

2019 ◽  
Vol 29 (12) ◽  
pp. 4598-4606 ◽  
Author(s):  
Abdul-Majid Wazwaz
Keyword(s):  
Direct Method ◽  
Soliton Solutions ◽  
Handling Time ◽  
Time Dependent ◽  
Specific Data ◽  
Integrable Equations ◽  
Content Type ◽  
Constant Coefficients ◽  
Multiple Complex Soliton Solutions ◽  
Practical Implications

Purpose The purpose of this paper is concerned with developing new integrable Vakhnenko–Parkes equations with time-dependent coefficients. The author obtains multiple soliton solutions and multiple complex soliton solutions for the time-dependent equations. Design/methodology/approach The developed time-dependent models have been handled by using the Hirota’s direct method. The author also uses Hirota’s complex criteria for deriving multiple complex soliton solutions. Findings The developed integrable models exhibit complete integrability for any analytic time-dependent coefficient. Research limitations/implications The paper presents an efficient algorithm for handling time-dependent integrable equations with time-dependent coefficients. Practical implications The author develops two Vakhnenko–Parkes equations with time-dependent coefficients. These models represent more specific data than the related equations with constant coefficients. The author showed that integrable equations with time-dependent coefficients give real and complex soliton solutions. Social implications The work presents useful techniques for finding integrable equations with time-dependent coefficients. Originality/value The paper gives new integrable Vakhnenko–Parkes equations, which give a variety of multiple real and complex soliton solutions.

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.

Painlevé analysis for three integrable shallow water waves equations with time-dependent coefficients

2019 ◽  
Vol 30 (2) ◽  
pp. 996-1008 ◽  
Author(s):  
Abdul-Majid Wazwaz
Keyword(s):  
Shallow Water ◽  
Water Waves ◽  
Direct Method ◽  
Soliton Solutions ◽  
Handling Time ◽  
Time Dependent ◽  
Shallow Water Waves ◽  
Integrable Equations ◽  
Content Type ◽  
Multiple Complex Soliton Solutions

Purpose The purpose of this paper is concerned with investigating three integrable shallow water waves equations with time-dependent coefficients. The author obtains multiple soliton solutions and multiple complex soliton solutions for these three models. Design/methodology/approach The newly developed equations with time-dependent coefficients have been handled by using Hirota’s direct method. The author also uses the complex Hirota’s criteria for deriving multiple complex soliton solutions. Findings The developed integrable models exhibit complete integrability for any analytic time-dependent coefficients defined though compatibility conditions. Research limitations/implications The paper presents an efficient algorithm for handling time-dependent integrable equations with analytic time-dependent coefficients. Practical implications This study introduces three new integrable shallow water waves equations with time-dependent coefficients. These models represent more specific data than the related equations with constant coefficients. The author shows that integrable equations with time-dependent coefficients give real and complex soliton solutions. Social implications The paper presents useful algorithms for finding integrable equations with time-dependent coefficients. Originality/value The paper presents an original work with a variety of 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.

A variety of completely integrable Calogero–Bogoyavlenskii–Schiff equations with time-dependent coefficients

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Abdul-Majid Wazwaz
Keyword(s):  
Soliton Solutions ◽  
Time Dependent ◽  
Integrable Equations ◽  
Content Type ◽  
Completely Integrable ◽  
Multiple Soliton Solutions ◽  
Simplified Hirota’S Method ◽  
Propagation Of Waves ◽  
Multiple Complex Soliton Solutions ◽  
Practical Implications

Purpose The purpose of this paper is to introduce a variety of new completely integrable Calogero–Bogoyavlenskii–Schiff (CBS) equations with time-dependent coefficients. The author obtains multiple soliton solutions and multiple complex soliton solutions for each of the developed models. Design/methodology/approach The newly developed models with time-dependent coefficients have been handled by using the simplified Hirota’s method. Moreover, multiple complex soliton solutions are derived by using complex Hirota’s criteria. Findings The developed models exhibit complete integrability, for specific determined functions, by investigating the compatibility conditions for each model. Research limitations/implications The paper presents an efficient algorithm for handling integrable equations with analytic time-dependent coefficients. Practical implications The work presents new integrable equations with a variety of time-dependent coefficients. The author showed that integrable equations with time-dependent coefficients give real and complex soliton solutions. Social implications This study presents useful algorithms for finding and studying integrable equations with time-dependent coefficients. Originality/value The paper gives new integrable CBS equations which appear in propagation of waves and provide a variety of multiple real and complex soliton solutions.

Two integrable third-order and fifth-order KdV equations with time-dependent coefficients

2019 ◽  
Vol 29 (6) ◽  
pp. 2093-2102 ◽  
Author(s):  
Abdul-Majid Wazwaz
Keyword(s):  
Efficient Algorithm ◽  
Soliton Solutions ◽  
Integrable Equation ◽  
Time Dependent ◽  
Integrable Equations ◽  
Content Type ◽  
Kdv Equations ◽  
Propagation Of Waves ◽  
Fifth Order ◽  
Multiple Complex Soliton Solutions

Purpose The purpose of this paper is concerned with developing two integrable Korteweg de-Vries (KdV) equations of third- and fifth-orders; each possesses time-dependent coefficients. The study shows that multiple soliton solutions exist and multiple complex soliton solutions exist for these two equations. Design/methodology/approach The integrability of each of the developed models has been confirmed by using the Painlev´e analysis. The author uses the complex forms of the simplified Hirota’s method to obtain two fundamentally different sets of solutions, multiple real and multiple complex soliton solutions for each model. Findings The time-dependent KdV equations feature interesting results in propagation of waves and fluid flow. Research limitations/implications The paper presents a new efficient algorithm for constructing time-dependent integrable equations. Practical implications The author develops two time-dependent integrable KdV equations of third- and fifth-order. These models represent more specific data than the constant equations. The author showed that integrable equation gives real and complex soliton solutions. Social implications The work presents useful findings in the propagation of waves. Originality/value The paper presents a new efficient algorithm for constructing time-dependent integrable equations.

An extended time-dependent KdV6 equation

2019 ◽  
Vol 29 (11) ◽  
pp. 4205-4212
Author(s):  
Abdul-Majid Wazwaz ◽  
Gui-Qiong Xu
Keyword(s):  
Direct Method ◽  
Soliton Solutions ◽  
Complete Integrability ◽  
Time Dependent ◽  
Content Type ◽  
Dependent Model ◽  
First Time ◽  
Multiple Complex Soliton Solutions ◽  
Kdv6 Equation ◽  
New Time

Purpose The purpose of this paper is to develop a new time-dependent KdV6 equation. The authors derive multiple soliton solutions and multiple complex soliton solutions for a time-dependent equation. Design/methodology/approach The newly developed time-dependent model has been handled by using the Hirota’s direct method. The authors also use the complex Hirota’s criteria for deriving multiple complex soliton solutions. Findings The examined extension of the KdV6 model exhibits complete integrability for any analytic time-dependent coefficient. Research limitations/implications The paper presents a new efficient algorithm for constructing extended models which give a variety of multiple real and complex soliton solutions. Practical implications The paper introduced a new time-dependent KdV6 equation, where integrability is emphasized for any analytic time-dependent function. Social implications The findings are new and promising. Multiple real and multiple complex soliton solutions were formally derived. Originality/value This is an entirely new work where a new time-dependent KdV6 equation is established. This is the first time that the KdV6 equation is examined as a time-dependent equation. Moreover, the complete integrability of this newly developed equation is emphasized via using Painlevé test.

A (2 + 1)-dimensional extension of the Benjamin-Ono equation

2018 ◽  
Vol 28 (11) ◽  
pp. 2681-2687 ◽  
Author(s):  
Abdul-Majid Wazwaz
Keyword(s):  
Soliton Solutions ◽  
Traveling Wave Solutions ◽  
Content Type ◽  
Multiple Soliton Solutions ◽  
Proposed Model ◽  
New Findings ◽  
Propagation Of Waves ◽  
Model Features ◽  
Multiple Complex Soliton Solutions ◽  
Practical Implications

Purpose The purpose of this paper is concerned with developing a (2 + 1)-dimensional Benjamin–Ono equation. The study shows that multiple soliton solutions exist and multiple complex soliton solutions exist for this equation. Design/methodology/approach The proposed model has been handled by using the Hirota’s method. Other techniques were used to obtain traveling wave solutions. Findings The examined extension of the Benjamin–Ono model features interesting results in propagation of waves and fluid flow. Research limitations/implications The paper presents a new efficient algorithm for constructing extended models which give a variety of multiple soliton solutions. Practical implications This work is entirely new and provides new findings, where although the new model gives multiple soliton solutions, it is nonintegrable. Originality/value The work develops two complete sets of multiple soliton solutions, the first set is real solitons, whereas the second set is complex solitons.

Assessing brand equity in the luxury wine market by exploiting tastemaker scores

2017 ◽  
Vol 26 (5) ◽  
pp. 447-452 ◽  
Author(s):  
Amanda J. Blair ◽  
Christina Atanasova ◽  
Leyland Pitt ◽  
Anthony Chan ◽  
Åsa Wallstrom
Keyword(s):  
Brand Equity ◽  
Design Methodology ◽  
Online Database ◽  
Initial Sample ◽  
Specific Data ◽  
Content Type ◽  
Financial Perspective ◽  
Branded Product ◽  
Wine Market ◽  
Practical Implications

Purpose Calculating brand equity, the price differential that a branded product is able to charge compared to an unbranded equivalent, often suffers from a lack of a means to truly determine equivalence. Luxury wines have the benefit of an established measure of equivalency – the Parker score. Robert Parker’s influence as a tastemaker provides a point of comparison across brands. This study looks at brand equity of Bordeaux classified growth wines considering château brands, growths and vintages to illustrate the intangible value for the consumer. Design/methodology/approach Using price and wine-specific data from Wine-Searcher.com, an online database and search engine, an initial sample of 393 wines with Parker scores ranging from 72 to 100 is presented. A subset of perfect wines, with 100-point Parker scores, is also reviewed focusing on the great vintage of 2009. Findings The results indicate that brand equity in the luxury wine market exists. Not only is this true for the brand of a specific château, but there is also equity associated with the vintage and the growth. Practical implications This offers practical implications for brand managers in positioning their wines. Originality/value An analysis of luxury wines supports the financial perspective on brand equity, especially when there is a viable means of determining equivalence, such as the Parker score.

The big data boost

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Keyword(s):  
Big Data ◽  
Competitive Advantage ◽  
Case Studies ◽  
Design Methodology ◽  
Reading Time ◽  
Specific Data ◽  
Content Type ◽  
Bulk Data ◽  
Pertinent Information ◽  
Practical Implications

Purpose This paper aims to review the latest management developments across the globe and pinpoint practical implications from cutting-edge research and case studies. Design/methodology/approach This briefing is prepared by an independent writer who adds their own impartial comments and places the articles in context. Findings Organizations of all sizes are looking to big data to boost competitive advantage and create sustained growth. Yet bulk data is not typically enough on its own, and proprietary applications and organizationally-specific data is required. Originality/value The briefing saves busy executives, strategists and researchers hours of reading time by selecting only the very best, most pertinent information and presenting it in a condensed and easy-to-digest format.

New (3+1)-dimensional integrable fourth-order nonlinear equation: lumps and multiple soliton solutions

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Abdul-Majid Wazwaz
Keyword(s):  
Fourth Order ◽  
Soliton Solutions ◽  
Integrable Equation ◽  
Lump Solutions ◽  
Content Type ◽  
Multiple Soliton Solutions ◽  
Order Nonlinear Equation ◽  
New Equation ◽  
Practical Implications

Purpose This paper aims to introduce a new (3 + 1)-dimensional fourth-order integrable equation characterized by second-order derivative in time t. The new equation models both right- and left-going waves in a like manner to the Boussinesq equation. Design/methodology/approach This formally uses the simplified Hirota’s method and lump schemes for determining multiple soliton solutions and lump solutions, which are rationally localized in all directions in space. Findings This paper confirms the complete integrability of the newly developed (3 + 1)-dimensional model in the Painevé sense. Research limitations/implications This paper addresses the integrability features of this model via using the Painlevé analysis. Practical implications This paper presents a variety of lump solutions via using a variety of numerical values of the included parameters. Social implications This work formally furnishes useful algorithms for extending integrable equations and for the determination of lump solutions. Originality/value To the best of the author’s knowledge, this paper introduces an original work with newly developed integrable equation and shows useful findings of solitons and lump solutions.

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