Approximate Hamiltonian Symmetry Groups and Recursion Operators for Perturbed Evolution Equations by M. Nadjafikhah, A. Mokhtary

“…Indeed, as a main consequence, this extended procedure is applied in order to compute the approximate conservation laws and approximate recursion operators corresponding to these types of equations. …”
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Noether and partial Noether approach for the nonlinear (3+1)-dimensional elastic wave equations. by Akhtar Hussain, M Usman, Fiazuddin Zaman, Ahmed M Zidan, Jorge Herrera

“…Instead, we used an extended approach based on the concept of a partial Lagrangian to uncover conservation laws. Both techniques account for the conservation laws of linear momentum and energy within the model. …”
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On Construction of a Super Hierarchy of the Wadati-Konno-Ichikawa Equation by Xuemei Li, Lutong Li

“…Infinitely, many conserved laws of the super WKI equation are constructed by using spectral parameter expansions.…”
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Numerical Feedback Stabilization with Applications to Networks by Simone Göttlich, Peter Schillen

“…The focus is on the numerical consideration of feedback boundary control problems for linear systems of conservation laws including source terms. We explain under which conditions the numerical discretization can be used to design feedback boundary values for network applications such as electric transmission lines or traffic flow systems. …”
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On the Splitting of the Einstein Field Equations with respect to General (1+3) Threading of Spacetime by Aurel Bejancu, Hani Reda Farran

“…Based on general (1+3) threading of the spacetime (M,g), we obtain a new and simple splitting of both the Einstein field equations (EFE) and the conservation laws in (M,g). As an application, we obtain the splitting of EFE in an almost FLRW universe with energy-momentum tensor of a perfect fluid. …”
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Bäcklund Transformation and Quasi-Periodic Solutions for a Variable-Coefficient Integrable Equation by Wenjuan Rui, Yufeng Zhang

“…Binary Bell polynomials are applied to construct bilinear formalism, bilinear Bäcklund transformation, Lax pair, and infinite conservation laws of the generalized variable-coefficient fifth-order Korteweg-de Vries equation. …”
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A Soliton Hierarchy Associated with a Spectral Problem of 2nd Degree in a Spectral Parameter and Its Bi-Hamiltonian Structure by Yuqin Yao, Shoufeng Shen, Wen-Xiu Ma

“…Bi-Hamiltonian structures of the presented soliton hierarchy are furnished by using the trace identity, and thus, all presented equations possess infinitely commuting many symmetries and conservation laws, which implies their Liouville integrability.…”
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Entropy Schemes for One-Dimensional Convection-Diffusion Equations by Rongsan Chen

“…In this paper, we extend the entropy scheme for hyperbolic conservation laws to one-dimensional convection-diffusion equation. …”
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Radiative Mixed Convection over an Isothermal Cone Embedded in a Porous Medium with Variable Permeability by M. F. El-Amin, N. A. Ebrahiem, Amgad Salama, Shuyu Sun

“…The transformed conservation laws are solved numerically for the case of variable surface temperature conditions. …”
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Bell Polynomials Approach Applied to (2 + 1)-Dimensional Variable-Coefficient Caudrey-Dodd-Gibbon-Kotera-Sawada Equation by Wen-guang Cheng, Biao Li, Yong Chen

“…Finally, the infinite conservation laws of this equation are obtained by decoupling binary Bell polynomials. …”
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Lie groups and continuum mechanics: where do we stand today? by de Saxcé, Géry, Razafindralandy, Dina

“…We consider the Lie symmetry group of the equations of a mechanical problem and investigate how to take advantage of them in developping analytical models (self-similar solutions, conservation laws, turbulence, ...) of the physical phenomena encoded in these equations. …”
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Time-Scale Version of Generalized Birkhoffian Mechanics and Its Symmetries and Conserved Quantities of Noether Type by Jin-Yue Chen, Yi Zhang

“…The time-scale version of Noether symmetry and conservation laws for three Birkhoffian mechanics, namely, nonshifted Birkhoffian systems, nonshifted generalized Birkhoffian systems, and nonshitfed constrained Birkhoffian systems, are studied. …”
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Hydrodynamic scaling limit of continuum solid-on-solid model by Anamaria Savu

“…What distinguishes our model from other models discussed so far is the presence of two conservation laws for the dynamics in a nonperiodic box and the complex dynamics that is not nearest-neighbor interaction. …”
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Exact Solution for Non-Self-Similar Wave-Interaction Problem during Two-Phase Four-Component Flow in Porous Media by S. Borazjani, P. Bedrikovetsky, R. Farajzadeh

“…We derive the exact solution for 3×3 hyperbolic system of conservation laws that corresponds to two-phase four-component flow in porous media where sorption of the third component depends on its own concentration in water and also on the fourth component concentration. …”
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A New Integro-Differential Equation for Rossby Solitary Waves with Topography Effect in Deep Rotational Fluids by Hongwei Yang, Qingfeng Zhao, Baoshu Yin, Huanhe Dong

“…By analyzing the equation, some conservation laws associated with Rossby solitary waves are derived. …”
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A Numerical Scheme Based on an Immersed Boundary Method for Compressible Turbulent Flows with Shocks: Application to Two-Dimensional Flows around Cylinders by Shun Takahashi, Taku Nonomura, Kota Fukuda

“…The turbulent flow region is modeled by a second-order pseudo skew-symmetric form with minimum dissipation, while the monotone upstream-centered scheme for conservation laws (MUSCL) scheme is employed in the shock region. …”
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Numerical Simulation of Unsteady Compressible Flow in Convergent Channel: Pressure Spectral Analysis by Petra Pořízková, Karel Kozel, Jaromír Horáček

“…Due to the motion of the grid, the basic system of conservation laws is considered in the arbitrary Lagrangian-Eulerian (ALE) form. …”
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Scalar Field Kantowski–Sachs Solutions in Teleparallel <i>F</i>(<i>T</i>) Gravity by Alexandre Landry

“…We begin by setting the exact field equations to be solved and solve conservation laws for possible scalar field potential, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>V</mi><mfenced open="(" close=")"><mi>ϕ</mi></mfenced></mrow></semantics></math></inline-formula>, solutions. …”
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Study of baryon-strangeness and charge-strangeness correlations in Pb–Pb collisions at √sNN = 5.02 TeV with ALICE by Saha Swati

“…Theoretical predictions from the Thermal-FIST model are compared with experimental results, providing insights into the effects of resonance decays and charge conservation laws on the correlations.…”
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Application of fluid dynamics in modeling the spatial spread of infectious diseases with low mortality rate: A study using MUSCL scheme by Nnaji Daniel Ugochukwu, Kiogora Phineas Roy, Onah Ifeanyi Sunday, Mung’atu Joseph, Aguegboh Nnaemeka Stanley

“…The Monotone Upwind Scheme for Conservation Laws is employed to enhance the accuracy of numerical solutions, providing a high-resolution approach for capturing disease transmission patterns. …”
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