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Formal Diagonalisation of Lax-Darboux Schemes
Моделирование и анализ информационных систем, 2015 We discuss the concept of Lax-Darboux scheme and illustrate it on well known examples associated with the Nonlinear Schro¨dinger (NLS) equation. We explore the Darboux links of the NLS hierarchy with the hierarchy of Heisenberg model, principal chiral ...
A. V. Mikhailov
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Mathematics, 2021 In this work, we study the generalized 2D equal-width equation which arises in various fields of science. With the aid of numerous methods which includes Lie symmetry analysis, power series expansion and Weierstrass method, we produce closed-form ...
Chaudry Masood Khalique, Karabo Plaatjie
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Mathematics, 2022 Invariant finite-difference schemes are considered for one-dimensional magnetohydrodynamics (MHD) equations in mass Lagrangian coordinates for the cases of finite and infinite conductivity.
Vladimir Dorodnitsyn, Evgeniy Kaptsov
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A proof of Kirchhoff's first law for hyperbolic conservation laws on networks
Networks and Heterogeneous Media, 2023 In dynamical systems on networks, Kirchhoff's first law describes the local conservation of a quantity across edges. Predominantly, Kirchhoff's first law has been conceived as a phenomenological law of continuum physics.
Alexandre M. Bayen +2 more
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Electromagnetic Signatures of Possible Charge Anomalies in Tunneling
Quantum Reports, 2022 We reconsider some well-known tunneling processes from the point of view of Aharonov-Bohm electrodynamics, a unique extension of Maxwell’s theory which admits charge-current sources that are not locally conserved.
Fernando Minotti, Giovanni Modanese
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Quantum Uncertainty and Energy Flux in Extended Electrodynamics
Quantum Reports, 2021 In quantum theory, for a system with macroscopic wavefunction, the charge density and current density are represented by non-commuting operators. It follows that the anomaly I=∂tρ+∇·j, being essentially a linear combination of these two operators in the ...
Fernando Minotti, Giovanni Modanese
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Ecosystem Health and Sustainability, 2022 The U.S. federal government’s requirements and guidance for wetland conservation are reflected in a series of federal laws, regulations, and policies.
Ligang Zhang +6 more
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On the structure of conservation laws of (3+1)-dimensional wave equation
Arab Journal of Mathematical Sciences, 2018 In this paper, a (3+1)-dimensional wave equation is studied from the point of view of Lie’s theory in partial differential equations including conservation laws.
S. Reza Hejazi, Elham Lashkarian
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Scaling Symmetries and Conservation Laws for Variable-coefficients Nonlinear Dispersive Equations
Trends in Computational and Applied Mathematics, 2019 Scaling symmetries arise in different branches of physics, and symmetry-based approaches are powerful tools for studying scaling-invariant models since they can provide conservation laws that are not obvious by inspection.
Érica M. Silva, Wescley L. Souza
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On the Conservation Laws and Exact Solutions of a Modified Hunter-Saxton Equation
Advances in Mathematical Physics, 2014 We study the modified Hunter-Saxton equation which arises in modelling of nematic liquid crystals. We obtain local conservation laws using the nonlocal conservation method and multiplier approach.
Sait San, Emrullah Yaşar
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