Lie symmetries of two-dimensional shallow water equations with variable bottom topography
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Publication:5129833
DOI10.1063/5.0007274zbMath1445.35279arXiv1911.02097OpenAlexW3102778836WikidataQ98203210 ScholiaQ98203210MaRDI QIDQ5129833
Roman O. Popovych, Alexander Bihlo, Nataliia Poltavets
Publication date: 2 November 2020
Published in: Chaos: An Interdisciplinary Journal of Nonlinear Science (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1911.02097
PDEs in connection with fluid mechanics (35Q35) Symmetry analysis, Lie group and Lie algebra methods applied to problems in fluid mechanics (76M60) Geophysical flows (76U60)
Related Items
Mapping method of group classification, Group classification and conservation laws of a class of hyperbolic equations, Lie symmetry analysis for two-phase flow with mass transfer, Conservative invariant finite‐difference schemes for the modified shallow water equations in Lagrangian coordinates, Semi-analytical solutions of shallow water waves with idealised bottom topographies, Point and generalized symmetries of the heat equation revisited, Lie group approach for constructing all reciprocal transformations: The two‐dimensional stationary gas dynamics equations, Lie group symmetry analysis and invariant difference schemes of the two-dimensional shallow water equations in Lagrangian coordinates, Similarity transformations for modified shallow water equations with density dependence on the average temperature, Realizations of Lie algebras on the line and the new group classification of (1+1)-dimensional generalized nonlinear Klein-Gordon equations
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Cites Work
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- Properties and exact solutions of the equations of motion of shallow water in a spinning paraboloid
- A guide to RBF-generated finite differences for nonlinear transport: shallow water simulations on a sphere
- Extended group analysis of variable coefficient reaction-diffusion equations with exponential nonlinearities
- Exact solutions of one-dimensional nonlinear shallow water equations over even and sloping bottoms
- Complete point symmetry group of the barotropic vorticity equation on a rotating sphere
- On symmetries and conservation laws of the equations of shallow water with an axisymmetric profile of bottom
- Group analysis of variable coefficient diffusion-convection equations. I: Enhanced group classification
- A finite element exterior calculus framework for the rotating shallow-water equations
- Group structure and the basis of conservation laws
- Enhanced group classification of gardner equations with time-dependent coefficients
- Admissible transformations and normalized classes of nonlinear Schrödinger equations
- Applications of symmetry methods to partial differential equations
- Nonlocal symmetries. Heuristic approach
- Algebraic method for group classification of \((1+1)\)-dimensional linear Schrödinger equations
- Lie symmetries of generalized Burgers equations: application to boundary-value problems
- Generalization of the algebraic method of group classification with application to nonlinear wave and elliptic equations
- On the geometry of extended self-similar solutions of the Airy shallow water equations
- Enhanced group classification of nonlinear diffusion-reaction equations with gradient-dependent diffusivity
- Symmetry analysis of a system of modified shallow-water equations
- Enhanced symmetry analysis of two-dimensional Burgers system
- On the group classification of variable-coefficient nonlinear diffusion--convection equations
- Symmetry preserving parameterization schemes
- Complete group classification of a class of nonlinear wave equations
- Point symmetry group of the barotropic vorticity equation
- New results on group classification of nonlinear diffusion–convection equations
- Group theoretical analysis of a rotating shallow liquid in a rigid container
- Solvable Lie algebras of dimension six
- Water waves of finite amplitude on a sloping beach
- Symmetry group analysis of the shallow water and semi-geostrophic equations
- The Multiplier Method to Construct Conservative Finite Difference Schemes for Ordinary and Partial Differential Equations
- Symmetries and exact solutions of the rotating shallow-water equations
- Some exact solutions to the nonlinear shallow-water wave equations
- Discrete point symmetries of ordinary differential equations
- How to construct the discrete symmetries of partial differential equations
- Invariant Discretization Schemes for the Shallow-Water Equations
- Zeroth‐order conservation laws of two‐dimensional shallow water equations with variable bottom topography
- Equivalence groupoid of a class of general Burgers-Korteweg-de Vries equations with space-dependent coefficients
- Group analysis of general Burgers–Korteweg–de Vries equations
- Symmetry-Preserving Numerical Schemes
- Computation of invariants of Lie algebras by means of moving frames
- Symmetries and differential equations
