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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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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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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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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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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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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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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Numerical analysis of a caprock integrity during oil production by steam-assisted gravity drainage method by Anastasiia Kostina, Maxim Zhelnin, Oleg Plekhov

“…The model includes mass conservation laws, the energy conservation law and the linear momentum balance. …”
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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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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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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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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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Approach in Theory of Nonlinear Evolution Equations: The Vakhnenko-Parkes Equation by V. O. Vakhnenko, E. J. Parkes

“…A Bäcklund transformation for the VPE is used to construct conservation laws. The standard IST method for third-order spectral problems is used to investigate solutions corresponding to bound states of the spectrum and to a continuous spectrum. …”
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Riemann problems with non--local point constraints and capacity drop by Boris Andreianov, Carlotta Donadello, Ulrich Razafison, Massimiliano D. Rosini

“…In the present note we discuss in details the Riemann problem for a one-dimensional hyperbolic conservation law subject to a point constraint. We investigate how the regularity of the constraint operator impacts the well--posedness of the problem, namely in the case, relevant for numerical applications, of a discretized exit capacity. …”
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Fractional Theoretical Model for Gravity Waves and Squall Line in Complex Atmospheric Motion by Liguo Chen, Liangui Yang

“…By obtaining the exact solution and the conservation laws, the fission properties of algebraic gravity solitary waves are discussed. …”
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On quasi-integrable deformation scheme of the KdV system by Kumar Abhinav, Partha Guha

“…The standard abelianization process based on the inherent sl(2) loop algebra leads to an infinite number of anomalous conservation laws, that yield conserved charges for definite space-time parity of the solution. …”
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Robust Diffeomorphic Mapping via Geodesically Controlled Active Shapes by Daniel J. Tward, Jun Ma, Michael I. Miller, Laurent Younes

“…This paper presents recent advances in the use of diffeomorphic active shapes which incorporate the conservation laws of large deformation diffeomorphic metric mapping. …”
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