On the Shallow Water Equations
Abstract
We studied the shallow water equations of nonlinear conservation laws. First we studied the parametrisation of nonlinear elementary waves and hence we present the solution to the Riemann problem. We also prove the uniqueness of the Riemann solution. The Riemann invariants are formulated. Moreover we give an interesting application of the Riemann invariants. We present the shallow water system in a diagonal form, which admits the existence of a global smooth solution for these equations. The other application is to introduce new conservation laws for the shallow water equations.
Acknowledgments:
The author wants to express deepest gratefulness to the editor and reviewers for valuable comments and suggestions.
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Artikel in diesem Heft
- Frontmatter
- Explicit Solutions and Conservation Laws of a Coupled Burgers’ Equation
- Residual Symmetry Analysis for Novel Localized Excitations of a (2+1)-Dimensional General Korteweg-de Vries System
- Mechanical, Electronic, and Optical Properties of β-B6O: First-Principles Calculations
- On a Super Generalized X-Dependent Hirota Equation
- The Slug and Churn Turbulence Characteristics of Oil–Gas–Water Flows in a Vertical Small Pipe
- Flow and Heat Transfer in a Newtonian Nanoliquid due to a Curved Stretching Sheet
- The Pressure Dependence of Structural, Electronic, Mechanical, Vibrational, and Thermodynamic Properties of Palladium-Based Heusler Alloys
- Exact Analysis of the Flow and Heat Transfer of the SA-TiO2 Non-Newtonian Nanofluid Between Two Coaxial Cylinders Through a Porous Medium
- The Residual Symmetry and Consistent Tanh Expansion for the Benney System
- On the Shallow Water Equations
- Letter
- Zero-Time Tunneling – Revisited
