arXiv subjects

Rajeswari Seshadri

Publications and source records attributed to Rajeswari Seshadri.

5 recordsLinked to original sources

arXiv2026

Lie symmetry, Painlevé analysis and Conservation laws for (1+2)-Dimensional Kudryashov-Sinelshchikov (KS) equation

The wave propagation of pressures in liquids that contain gas bubbles are an important concern in fluid dynamics and mathematical physics. The Kudryashov Sinelshchikov equation offers a useful mathematical framework in the study of nonlinear wave motion in bubbly liquids with reference to the effects of viscosity and heat exchange between liquid and gaseous phases. This paper examines the dimensional reduced (1 + 2)-dimensional Kudryashov Sinelshchikov equation, a fourth-order nonlinear partial differential equation. Analyzing the Lie symmetry, an infinite dimension Lie algebra is obtained because of the presence of arbitrary functions. By applying the commutative relation between these vector fields and choosing the specific forms for the arbitrary functions, helps the governing PDE to reduce to fourth order ODEs. The reduced equations are then investigated using the Painleve analysis to give solutions in the form of Laurent series. In addition, multiplier approach is used to obtain the conserved vectors and to analyzed conservations properties of the equation. We obtain four cases and the Conservation laws were verified for all the cases.

nlin.SI↗

arXiv2026

Painlevé Integrability, Auto-Bäcklund Transformation and the exact solutions of (1+2) Kudryashov-Sinelshchikov (KS) equation

In this research work, we consider a nonlinear fourth-order (1+2)-dimensional Kudryashov-Sinelshchikov (KS) equation which represents the wave propagation of pressures in liquids that contain gas bubbles. A direct Integrability of the KS equation is analysed using Painleve Analysis with Singular Manifold Method (SMM). With the help of WTC algorithm, we show that the (1+2) KS equation is Painleve integrable. Then by truncating the Painleve expansion we obtain the Auto-Backlund Transformation (ABT). By taking suitable forms of Manifold, various exact solutions based on the obtained Auto-Backlund transformation are derived. The consistancy check for these solutions are also performed. Representative solutions are presented in the from of 2D and 3D plots to understand the geometric perspective of the solutions.

nlin.SI↗

arXiv2026

Classical Symmetries and Painleve Analysis for the (1+3) Kudryashov-Sinelshchikov Equation

The integrability of the Kudryashov-Sinelshchikov equation in (1+3) dimension is detected using its point symmetries and the Singularity analysis method. The symmetries mostly points to the existence of infinite-dimensional Lie algebra with the presence of mostly arbitrary functions. The reduction process is initiated by considering these arbitrary functions in the general symmetry vectors. For certain functions, trivial solutions for the general parent equation is obtained whereas for some of the functions, the reductions does not yield an unmitigated result. Finally, a positive result is listed for one of the arbitrary function, for which the singularity analysis method is employed to study the Painleve property. The resultant PDE happens to be a fourth-order equation and its approval of the Painleve property hints at the integrability of the Kudryashov- Sinelshchikov equation in the general case.

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arXiv2023

Symmetries and Lie Algebra of Ramanujan Equation

Symmetry analysis of Ramanujan's system of differential equations is performed by representing it as a third-order equation. A new system consisting of a second-order and a first-order equation is derived from Ramanujan's system. The Lie algebra of the new system is equivalent to the algebra of the third-order equation. This forms the basis of our intuition that for a system of first-order odes its infinite-dimensional algebra of symmetries contains a subalgebra which is a representation of the Lie algebra for any system or differential equation which can be obtained from the original system, even though the transformations are not point.

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arXiv2020

Lie Symmetry Analysis and Similarity Solutions for the Jimbo-Miwa Equation and Generalisations

We study the Jimbo-Miwa equation and two of its extended forms, as proposed by Wazwaz et al, using Lie's group approach. Interestingly, the travelling-wave solutions for all the three equations are similar. Moreover, we obtain certain new reductions which are completely different for each of the three equations. For example, for one of the extended forms of the Jimbo-Miwa equation, the subsequent reductions leads to a second-order equation with Hypergeometric solutions. In certain reductions, we obtain simpler first-order and linearisable second-order equations, which helps us to construct the analytic solution as a closed-form function. The variation in the nonzero Lie brackets for each of the different forms of the Jimbo-Miwa also presents a different perspective. Finally, singularity analysis is applied in order to determine the integrability of the reduced equations and of the different forms of the Jimbo-Miwa equation.

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