Publications (13)
1-Multisoliton and other invariant solutions of combined KdV - nKdV equation by using symmetry approach
Sachin Kumar, Dharmendra Kumar
Lie symmetry method is applied to investigate symmetries of the combined KdV-nKdV equation, that is a new integrable equation by combining the KdV equation and negative order KdV e…
BMO estimates for Hodge-Maxwell systems with discontinuous anisotropic coefficients
Dharmendra Kumar, Swarnendu Sil
We prove up to the boundary estimates for linear Maxwell-Hodge type systems for -valued differential -forms in dimensions \begin{align*} \…
Existence of variational solutions to doubly nonlinear nonlocal evolution equations via minimizing movements
Suchandan Ghosh, Dharmendra Kumar, Harsh Prasad +1
We prove existence of variational solutions for a class of doubly nonlinear nonlocal evolution equations whose prototype is the double phase equation \begin{align*} \partial_t u^m…
On Fault-Tolerant Design of Exclusive-OR Gates in QCA
Dharmendra Kumar, Debasis Mitra, Bhargab B. Bhattacharya
Design paradigms of logic circuits with Quantum-dot Cellular Automata (QCA) have been extensively studied in the recent past. Unfortunately, due to the lack of mature fabrication s…
Carleman estimates for sub-Laplacians on Carnot groups
Vedansh Arya, Dharmendra Kumar
In this note, we establish a new Carleman estimate with singular weights for the sub-Laplacian on a Carnot group for functions satisfying the discrepancy assumption in…
Quintessential Implications of the presence of AdS in the Dark Energy sector
Purba Mukherjee, Dharmendra Kumar, Anjan A Sen
We explore the implications for an Anti-de Sitter (AdS) vacuum, equivalently a negative cosmological constant (nCC), in the dark energy (DE) sector using current cosmological obser…
Optimization of magneto-electric properties in Lead-free (x)Co1.2Ti0.2Fe1.6O4 - (100-x)BaTiO3 based composites
Rajeev Dwivedi, Samanway Mohanta, Ashutosh Anand +7
The paper investigates lead‑free multiferroic composites made of Co‑Ti‑Fe oxide and BaTiO3, studying how composition and sintering temperature affect their structural, dielectric,…
Lie symmetry analysis and new periodic solitary wave solutions of (3+1)-dimensional generalized shallow water wave equation
Sachin Kumar, Dharmendra Kumar
Many important physical situations such as fluid flows, marine environment, solid-state physics and plasma physics have been represented by shallow water wave equation. In this art…
New solitary wave and Multiple soliton solutions of (3 + 1)-dimensional KdV type equation by using Lie symmetry approach
Sachin Kumar, Dharmendra Kumar
Solitary waves are localized gravity waves that preserve their consistency and henceforth their visibility through properties of nonlinear hydrodynamics. Solitary waves have finite…
Exploring Alternative Cosmologies with the LSST: Simulated Forecasts and Current Observational Constraints
Dharmendra Kumar, Ayan Mitra, Shahnawaz A. Adil +1
In recent years, the Lambda Cold Dark Matter (LCDM) model, which has been pivotal in cosmological studies, has faced significant challenges due to emerging observational and theore…
Investigation of Softer Lattice Dynamics in Defect Engineered GeTe Crystals
Saptak Majumder, Pintu Singha, Sharath Kumar C. +7
The impact of Ge vacancies on the low-temperature lattice dynamics of single-crystalline GeTe was investigated through a comparative study of two off-stoichiometric samples: Ge$_{0…
Borderline gradient continuity for fractional heat type operators
Vedansh Arya, Dharmendra Kumar
In this paper, we establish gradient continuity for solutions to \[ (\partial_t - \operatorname{div}(A(x) \nabla u))^s =f,\ s \in (1/2, 1), \] when belongs to the scaling criti…
Boundary differentiability of solutions to elliptic equations in convex domains in the borderline case
Dharmendra Kumar
In this work, we consider the following elliptic partial differential equations: \begin{equation*} \left\{ \begin{aligned}{} - b_{ij} \; \frac{\partial^{2} w}{\partial x_{i} \parti…