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Invariant conservation law-preserving discretizations of linear and nonlinear wave equations [PDF]
Journal of Mathematics and Physics, 2020 Symmetry- and conservation law-preserving finite difference discretizations are obtained for linear and nonlinear one-dimensional wave equations on five- and nine-point stencils using the theory of Lie point symmetries of difference equations and the ...
A. Cheviakov, V. Dorodnitsyn, E. Kaptsov
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Lie symmetry reductions and exact solutions to a generalized two-component Hunter-Saxton system
AIMS Mathematics, 2021 Based on the classical Lie group method, a generalized two-component Hunter-Saxton system is studied in this paper. All of the its geometric vector fields, infinitesimal generators and the commutation relations of Lie algebra are derived.
Huizhang Yang, Wei Liu, Yunmei Zhao
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Computation of $\mu$-symmetry and $\mu$-conservation law for the Camassa-Holm and Hunter-Saxton equations [PDF]
AUT Journal of Mathematics and Computing, 2023 This work is intended to compute the $\mu$-symmetry and $\mu$-conservation laws for the Cammasa-Holm (CH) equation and the Hunter-Saxton (HS) equation. In other words, $\mu$-symmetry, $\mu$-symmetry reduction, variational problem, and $\mu$-conservation ...
Somayeh Shaban, Mehdi Nadjafikhah
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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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Neural Conservation Laws: A Divergence-Free Perspective [PDF]
Neural Information Processing Systems, 2022 We investigate the parameterization of deep neural networks that by design satisfy the continuity equation, a fundamental conservation law. This is enabled by the observation that any solution of the continuity equation can be represented as a divergence-
Jack Richter-Powell +2 more
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Ukrainian Journal of Physical Optics, 2021 . We recover the cases of solutions in the shape of bright, dark and singular optical solitons for the self-phase modulation effect, which belongs to the type of N. A. Kudryashov’s sextic power-law nonlinearity of refractive index.
E. Zayed +7 more
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Jurnal Ilmu Kehutanan, 2021 Law enforcement plays a vital role to prevent the extinction of endangered species, including the Sumatran tiger. We investigated the roles of private sector involvement in Tambling Wildlife Nature Conservation (TWNC) for supporting law enforcement by ...
Ardi Bayu Firmansyah +5 more
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On the Incompleteness of Ibragimov's Conservation Law Theorem and Its Equivalence to a Standard Formula Using Symmetries and Adjoint-Symmetries [PDF]
Symmetry, 2016 A conservation law theorem stated by N. Ibragimov along with its subsequent extensions are shown to be a special case of a standard formula that uses a pair consisting of a symmetry and an adjoint-symmetry to produce a conservation law through a well ...
S. Anco
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Split-step quintic B-spline collocation methods for nonlinear Schrödinger equations
AIMS Mathematics, 2023 Split-step quintic B-spline collocation (SS5BC) methods are constructed for nonlinear Schrödinger equations in one, two and three dimensions in this paper.
Shanshan Wang
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Output Feedback Stabilization for a Scalar Conservation Law with a Nonlocal Velocity [PDF]
SIAM Journal on Mathematical Analysis, 2013 In this paper, we study the output feedback stabilization for a scalar conservation law with a nonlocal velocity that models a highly re-entrant manufacturing system as encountered in semiconductor production.
J. Coron, Zhiqiang Wang
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