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LIE SYMMETRY ANALYSIS, PARAMETRIC REDUCTION AND CONSERVATION LAWS OF (3+1) DIMENSIONAL NONLINEAR DISPERSIVE SOLITON EQUATION

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arXiv 2025年

作者： Singhal, Anshika Joshi, Urvashi Arora, Rajan Department of Applied Mathematics and Scientific Computing Indian Institute of Technology Roorkee India

The core focus of this research work is to obtain invariant solutions and conservation laws of the (3+1)-dimensional Zakharov–Kuznetsov (ZK) equation which describes the phenomenon of wave stability and solitons propagation. ZK equation is significant in fluid dynamics, nonlinear optics, and acoustics. ZK equation plays an important role in understanding the behavior of nonlinear, dispersive waves especially in the presence of the magnetic field. Lie symmetry analysis has been applied to the (3+1)-dimensional ZK equation to derive invariant solutions. These solutions reveal how waves retain their shape as they travel, how they interact in space, and the impact of magnetic fields on wave propagation. Using the Lie symmetry, the (3+1) dimensional Zakharov-Kuznetsov equation is reduced to various ordinary differential equations. It also concludes with the conservation laws and non-linear self-adjointness property. Additionally, we align our findings with real-life problems, namely plasma physics, electromagnetic wave propagation, and water wave dynamics, providing the applicability of our theoretical results. Copyright © 2025, The Authors. All rights reserved.

关键词： Electromagnetic wave propagation in plasma

Modified Dai-Liao Spectral Conjugate Gradient Method with Application to Signal Processing

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arXiv 2025年

作者： Sahu, D.R. Sharma, Shikher Gautam, Pankaj Department of Mathematics Banaras Hindu University India Department of Applied Mathematics and Scientific Computing Indian Institute of Technology Roorkee India

In this article, we present a modified variant of the Dai-Liao spectral conjugate gradient method, developed through an analysis of eigenvalues and inspired by a modified secant condition. We show that the proposed method is globally convergent for general nonlinear functions under standard assumptions. By incorporating the new secant condition and a quasi-Newton direction, we introduce updated spectral parameters. These changes ensure that the resulting search direction satisfies the sufficient descent property without relying on any line search. Numerical experiments show that the proposed algorithm performs better than several existing methods in terms of convergence speed and computational efficiency. Its effectiveness is further demonstrated through an application in signal processing. © 2025, CC BY.

关键词： Conjugate gradient method

Analysis of magnetogasdynamic shock wave in a self-gravitating non-ideal dusty gas using Lie group theory

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Physics of Fluids 2025年第4期37卷

作者： Bhardwaj, Akshita Singh, Deepika Arora, Rajan Department of Applied Mathematics and Scientific Computing Indian Institute of Technology Roorkee Roorkee India Department of Mathematics Netaji Subhas University of Technology New Delhi India

This study delves into the behavior of a one-dimensional, unsteady flow following a shock wave in a non-ideal dusty gas, including an axial magnetic field and gravitational field. The Lie group theoretic method has been used to discuss all possible cases of the self-similarity solutions, for the considered problem in the medium of uniform density. This model has implications for astrophysical and laboratory plasma systems. The arbitrary constants in the Lie group generators yield solutions with power-law and exponential-law shock paths. The graphs of the reduced flow variables have been analyzed to study how they vary behind the shock front concerning the physical parameters like non-ideal parameter ( b ¯ ) , adiabatic exponent ( γ ) , gravitational parameter ( g 0 ) , the ratio of the density of solid particles to the initial density of the gas ( η 0 ) , Alfvén-Mach number ( M a − 2 ) , and geometric variation index ( ν ) . We investigate a detailed comparison between adiabatic and isothermal flow conditions. In isothermal case, the increase in fluid velocity and magnetic field suggests a comparatively accelerated and dynamic flow. Meanwhile, the decrease in density and pressure implies a more expansion and less compression state compared to the adiabatic case. The research concludes with an analysis of flow variable behavior under different physical conditions. © 2025 Author(s).

关键词： Lie groups

EXPERIMENTAL ANALYSIS OF MICROSCOPIC SPRAY PROPERTIES OF NONSTABILIZED WATER-IN-GASOLINE EMULSIONS USING SHADOWGRAPH IMAGING

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Atomization and Sprays 2025年第3期35卷 55-79页

作者： Schier, L. Blau, Benjamin Heinrich, C. Klein, Markus Institute of Automotive Technology Trier University of Applied Sciences TrierD-54293 Germany Institute of Applied Mathematics and Scientific Computing University of the Bundeswehr Munich NeubibergD-85579 Germany

In this study, the atomization of gasoline, water, and nonstabilized water-in-gasoline emulsions injected via a multihole gasoline direct injection (GDI) injector was investigated using shadowgraph imaging. The investigations were conducted in a single spray plume of the injector mounted in a constant-volume chamber. The parameters varied were the injection pressure, the emulsion compo-sition, and the measurement location. The comparison of emulsions of varying composition with the neat liquids revealed unexpected behavior. The Sauter mean diameter d32 of the emulsion spray exhibited only a marginal change when the water content was increased, although water and gasoline exhibited significant differences in surface tension, and the emulsion viscosity is expected to grow exponentially with increasing water fraction. Important findings are also presented for the variation of the measurement location within the spray plume. Axially, d32 increases with increasing distance from the injector, which is attributed to ongoing secondary break-up processes. Coherent structures and ligaments disintegrate into large droplets with progressing axial distance, which then disperse radially due to jet expansion, increasing d32 globally. Radially, d32 initially decreases because larger droplets remain closer to the axis due to higher inertia, while smaller droplets disperse throughout the entire spray. This initial decrease is followed by an increase until d32 reaches its maximum at the spray edge. © 2025 by Begell House, Inc.

关键词： Gasoline

Parameter identification in PDEs by the solution of monotone inclusion problems

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Numerische Mathematik 2025年 1-31页

作者： Gautam, Pankaj Grasmair, Markus Department of Applied Mathematics and Scientific Computing Indian Institute of Technology Roorkee Uttarakhand India Department of Mathematical Sciences Norwegian University of Science and Technology Trondheim Norway

In this paper we consider the solution of monotone inverse problems using the particular example of a parameter identification problem for a semilinear parabolic PDE. For the regularized solution of this problem, we introduce a total variation based regularization method requiring the solution of a monotone inclusion problem. We show well-posedness in the sense of inverse problems of the resulting regularization scheme. In addition, we introduce and analyze a numerical algorithm for the solution of this inclusion problem using a nested inertial primal dual method. We demonstrate by means of numerical examples the convergence of both the numerical algorithm and the regularization method.

关键词：

ON THE SEPARATING NOETHER NUMBER OF FINITE ABELIAN GROUPS

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arXiv 2025年

作者： Zhao, Kevin Zhong, Qinghai School of Mathematics and Statistics Nanning Normal University Nanning530100 China Center for Applied Mathematics of Guangxi Nanning Normal University Nanning530100 China Institute of Mathematics and Scientific Computing Heinrichstraße 36 Graz8010 Austria

The separating Noether number βsep(G) of a finite group G is the minimal positive integer d such that for every G-module V there is a separating set of degree ≤ d. In this manuscript, we investigate the separating Noether number βsep(G). Among others, we obtain the exact value of βsep(G) for finite abelian groups G, when either G is a p-group or r(G) ∊ {3, 5}.MSC Codes 13A50, 11B75, 20D60 Copyright © 2025, The Authors. All rights reserved.

关键词： Integer linear programming

A New Polynomial Reconstruction Scheme Aeno-C for Ader Methods to Very-High Orders of Accuracy

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SSRN

SSRN 2025年

作者： Yajaman, Siddharth Toro, Eleuterio F. Dematte, Riccardo Laboratory for Scientific Computing University of Cambridge Cambridge United Kingdom Laboratory of Applied Mathematics University of Trento Trento Italy University of Toronto Institute for Aerospace Studies Toronto Canada

In this paper, we introduce AENO-C, a high-order polynomial reconstruction scheme that builds upon AENO by employing a special averaging of the ENO polynomial and a conservative polynomial from the centered stencil closest to the ENO stencil, using a new joining function with improved asymptotic properties. The scheme is systematically evaluated within the ADER finite volume framework up to tenth-order accuracy on test cases involving the linear advection equation, Burgers’ equation with a source term, and the Euler equations. It is found to perform highly satisfactorily across different scenarios, including both smooth and discontinuous profiles, and for all considered orders of accuracy. For smooth solutions, it exhibits convergence rates clearly superior to ENO and the original AENO, making it competitive and, in many situations, even more efficient than WENO in achieving a given error tolerance. For discontinuous solutions, it demonstrates remarkable robustness, effectively resolving complex features with high fidelity while preventing the appearance of spurious oscillations. The new reconstruction scheme is simple to implement, computationally cheap, comparable to ENO and AENO, and provides a closed form polynomial expression which can be evaluated at any desired point. © 2025, The Authors. All rights reserved.

关键词： Euler equations

High order positivity-preserving numerical methods for a non-local photochemical model

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arXiv 2025年

作者： Pezzella, Mario National Research Council of Italy Institute for Applied Mathematics Mauro Picone Via P. Castellino Naples111 - 80131 Italy Italian National Group for Scientific Computing GNCS The National Institute for Advanced Mathematics INdAM Italy

In this paper we design high-order positivity-preserving approximation schemes for an integro-differential model describing photochemical reactions. Specifically, we introduce and analyze three classes of dynamically consistent methods, encompassing non-standard finite difference schemes, direct quadrature techniques and predictor-corrector approaches. The proposed discretizations guarantee the positivity, monotonicity and boundedness of the solution regardless of the temporal, spatial and frequency stepsizes. Comprehensive numerical experiments confirm the theoretical findings and demonstrate the efficacy of the proposed methods in simulating realistic photochemical *** Codes 65R20, 65M15, 65G99, 65Z05, 47H07, 45K05 © 2025, CC BY.

关键词： Numerical methods

Nonlocal perimeters and variations: Extremality and decomposability for finite and infinite horizons

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arXiv 2025年

作者： Carioni, Marcello Del Grande, Leonardo Iglesias, José A. Schönberger, Hidde Department of Applied Mathematics University of Twente Enschede7500AE Netherlands Institute of Analysis and Scientific Computing TU Wien Wiedner Hauptstrasse 8-10 ViennaA-1040 Austria

We analyze the extremality and decomposability properties with respect to two types of nonlocal perimeters available in the literature, the Gagliardo perimeter based on the eponymous seminorms and the nonlocal distributional Caccioppoli perimeter, both with finite and infinite interaction ranges. A nonlocal notion of indecomposability associated to these perimeters is introduced, and we prove that in both cases it can be characterized solely in terms of the interaction range or horizon Ε. Utilizing this, we show that it is possible to uniquely decompose a set into its Ε-connected components, establishing a nonlocal analogue of the decomposition theorem of Ambrosio, Caselles, Masnou and Morel. Moreover, the extreme points of the balls induced by the Gagliardo and nonlocal total variation seminorm are identified, which naturally correspond to the two nonlocal perimeters. Surprisingly, while the extreme points in the former case are normalized indicator functions of Ε-simple sets, akin to the classical TV-ball, in the latter case they are instead obtained from a nonlocal transformation applied to the extreme points of the TV-ball. Finally, we explore the nonlocal-to-local transition via a Γ-limit as Ε → 0 for both perimeters, recovering the classical Caccioppoli *** Codes 46A55, 35R11, 26B30, 49Q20 Copyright © 2025, The Authors. All rights reserved.

关键词： Disposability