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SYMMETRY AND CONSERVATION LAWS [PDF]
Proceedings of the National Academy of Sciences, 1964 Symmetry and invariance considerations, and even conservation laws, played undoubtedly an important role in the thinking of the early physicists, such as Galileo and Newton, and probably even before then. However, these considerations were not thought to be particularly important and were articulated only rarely.
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A Time Two-Mesh Compact Difference Method for the One-Dimensional Nonlinear Schrödinger Equation
Entropy, 2022 The nonlinear Schrödinger equation is an important model equation in the study of quantum states of physical systems. To improve the computing efficiency, a fast algorithm based on the time two-mesh high-order compact difference scheme for solving the ...
Siriguleng He, Yang Liu, Hong Li
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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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Symmetry Analysis and Conservation Laws for a Time-Fractional Generalized Porous Media Equation
Mathematics, 2022 The symmetry group method is applied to study a class of time-fractional generalized porous media equations with Riemann–Liouville fractional derivatives. All point symmetry groups and the corresponding optimal subgroups are determined.
Tianhang Gong, Wei Feng, Songlin Zhao
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A Time Two-Mesh Finite Difference Numerical Scheme for the Symmetric Regularized Long Wave Equation
Fractal and Fractional, 2023 The symmetric regularized long wave (SRLW) equation is a mathematical model used in many areas of physics; the solution of the SRLW equation can accurately describe the behavior of long waves in shallow water. To approximate the solutions of the equation,
Jingying Gao +3 more
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Scaling Symmetry and a New Conservation Law of the Harry Dym Equation [PDF]
Mathematics Interdisciplinary Research, 2021 In this paper, we obtain a new conservation law for the Harry Dym equation by using the scaling method. This method is algorithmic and based on variational calculus and linear algebra. In this method, the density of the conservation law is constructed by
Mehdi Jafari +2 more
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Getting deeper insight into stopping power problems in radiation physics using the Noether's theorem corollary [PDF]
Nuclear Technology and Radiation Protection, 2014 The theories that combine two different approaches in dealing with interacting objects, for instance, treating electromagnetic laser field classically, and the interacting atom as a quantum object, have some ambiguities and, as such, they should
Ristić Vladimir M. +3 more
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Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki, 2020 A nonlinear two-dimensional orthotropic filtration equation with the Riemann–Liouville time-fractional derivative is considered. It is proved that this equation can admits only linear autonomous groups of point transformations.
Veronika Olegovna Lukashchuk +1 more
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Hamiltonians of the Generalized Nonlinear Schrödinger Equations
Mathematics, 2023 Some types of the generalized nonlinear Schrödinger equation of the second, fourth and sixth order are considered. The Cauchy problem for equations in the general case cannot be solved by the inverse scattering transform. The main objective of this paper
Nikolay A. Kudryashov
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Blowup for Systems of Conservation Laws [PDF]
SIAM Journal on Mathematical Analysis, 2000 The author considers an initial value problem for a system of conservation laws \(U_t+ F(U)_x= 0\), \(U(x,0)= U_0(x)\), where \(U= U(x,t)\in \mathbb{R}^3\), \(F: \mathbb{R}^3\to \mathbb{R}^3\) is smooth and strictly hyperbolic. It is presented a class of \(3\times 3\)-systems for which one can prescribe initial data such that the solution blows up in ...
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