Author

# B. Mayil Vaganan

Other affiliations: K. L. N. College of Engineering, Indian Institute of Science

Bio: B. Mayil Vaganan is an academic researcher from Madurai Kamaraj University. The author has contributed to research in topics: Burgers' equation & Partial differential equation. The author has an hindex of 8, co-authored 20 publications receiving 127 citations. Previous affiliations of B. Mayil Vaganan include K. L. N. College of Engineering & Indian Institute of Science.

##### Papers

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TL;DR: It is shown here that generalized KdV equations are characterized by Euler–Painleve equations, and a plethora of exact, explicit similarity solutions are found which include inverse of hypergeometric function.

23 citations

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TL;DR: The generalized Burgers equation with linear damping and variable viscosity was subjected to Lie's classical method in this article, and five distinct expressions for the variable viscousity were identified.

Abstract: The generalized Burgers equation with linear damping and variable viscosity is subjected to Lie's classical method. Five distinct expressions for the variable viscosity are identified. Both the reduced ordinary differential equations and their corresponding Euler-Painleve transcendents admit first integrals in the form of Bernoulli's equation and are linearized to obtain solutions in closed form.

20 citations

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TL;DR: In this article, a generalized Burgers equation is linearized to Kummer's equation and the large time behavior of solutions of the GBE is determined, some exact closed form solutions are also found.

Abstract: Through a Cole-Hopf like transformation a generalized Burgers equation is linearized to Kummer's equation. The large time behaviour of solutions of the GBE is determined. Some exact closed form solutions are also found.

16 citations

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TL;DR: In this paper, the authors constructed large-time asymptotic solutions of generalized Burgers equations with periodic initial conditions by using a balancing argument and validated these results by a careful numerical study.

Abstract: In this paper, we construct large-time asymptotic solutions of some generalized Burgers equations with periodic initial conditions by using a balancing argument. These asymptotics are validated by a careful numerical study. We also show that our asymptotic results agree with the approximate solutions obtained by Parker [1] in certain limits.

10 citations

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TL;DR: In this paper, the similarity variables of the generalized Burgers equation were reported as an incomplete gamma function and also as a power of x/√t, and a perturbation solution of an Euler-Painleve transcedent.

Abstract: Similarity reductions of the generalized Burgers equation u t + u n u x + (j/2t + α) u + (β + y/x)u n+1 = u xx , where α, β, and y are non-negative constants, n a positive integer and j = 0, 1, 2, are obtained by the direct method of Clarkson and Kruskal [1]. This is the first work to report the similarity variables as an incomplete gamma function and also as a power of x/√t, and to provide a perturbation solution of an Euler-Painleve transcedent.

10 citations

##### Cited by

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TL;DR: To the best of our knowledge, there is only one application of mathematical modelling to face recognition as mentioned in this paper, and it is a face recognition problem that scarcely clamoured for attention before the computer age but, having surfaced, has attracted the attention of some fine minds.

Abstract: to be done in this area. Face recognition is a problem that scarcely clamoured for attention before the computer age but, having surfaced, has involved a wide range of techniques and has attracted the attention of some fine minds (David Mumford was a Fields Medallist in 1974). This singular application of mathematical modelling to a messy applied problem of obvious utility and importance but with no unique solution is a pretty one to share with students: perhaps, returning to the source of our opening quotation, we may invert Duncan's earlier observation, 'There is an art to find the mind's construction in the face!'.

3,015 citations

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TL;DR: In this paper, an exact solitary wave solution of the Korteweg-de Vries equation with power law nonlinearity with time-dependent coefficients of the nonlinear as well as the dispersion terms was obtained.

Abstract: This paper obtains an exact solitary wave solution of the Korteweg–de Vries equation with power law nonlinearity with time-dependent coefficients of the nonlinear as well as the dispersion terms. In addition, there are time-dependent damping and dispersion terms. The solitary wave ansatz is used to carry out the analysis. It is only necessary for the time-dependent coefficients to be Riemann integrable. As an example, the solution of the special case of cylindrical KdV equation falls out.

90 citations

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TL;DR: The objectives of this paper are to discuss the recent developments in mathematical modelling of Burgers’ equation, and throw some light on the plethora of challenges which need to be overcome in the research areas and give motivation for the next breakthrough to take place in a numerical simulation of ordinary / partial differential equations.

Abstract: Even if numerical simulation of the Burgers’ equation is well documented in the literature, a detailed literature survey indicates that gaps still exist for comparative discussion regarding the physical and mathematical significance of the Burgers’ equation. Recently, an increasing interest has been developed within the scientific community, for studying non-linear convective–diffusive partial differential equations partly due to the tremendous improvement in computational capacity. Burgers’ equation whose exact solution is well known, is one of the famous non-linear partial differential equations which is suitable for the analysis of various important areas. A brief historical review of not only the mathematical, but also the physical significance of the solution of Burgers’ equation is presented, emphasising current research strategies, and the challenges that remain regarding the accuracy, stability and convergence of various schemes are discussed. One of the objectives of this paper is to discuss the recent developments in mathematical modelling of Burgers’ equation and thus open doors for improvement. No claim is made that the content of the paper is new. However, it is a sincere effort to outline the physical and mathematical importance of Burgers’ equation in the most simplified ways. We throw some light on the plethora of challenges which need to be overcome in the research areas and give motivation for the next breakthrough to take place in a numerical simulation of ordinary / partial differential equations.

66 citations

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TL;DR: In this paper, the authors investigated admissible point transformations in classes of generalized KdV equations, obtained the necessary and sufficient conditions of similarity of such equations to the standard KDV and mKDV equations and carried out the exhaustive group classification of a class of variable-coefficient KdVM equations.

64 citations

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TL;DR: In this article, the solitary wave solution of the generalized KdV equation is obtained in the presence of time-dependent damping and dispersion, using a solitary wave ansatze that leads to the exact solution.

62 citations