Linear and nonlinear waves

By L. Chambers. Mathematical Gazette, 2000

2,101 citations recorded by the source corpus.

Subfields: Electrical and Electronic Engineering, Geophysics, Oceanography

View Paper: https://www.semanticscholar.org/paper/87dcc30928ea33d076ee42cdad4f1243751d2f48

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Citations in the corpus

Shock waves and blow-up phenomena for the periodic Degasperis-Procesi equation (2007, background): “It is also observed that the KdV equation does not accomodate wave breaking (by wave breaking we mean the phenomenon that a wave remains bounded but its slope becomes unbounded in finite time, see [43]).”
Numerical error estimation for nonlinear hyperbolic PDEs via nonlinear error transport (2011, methodology): “Solutions can be constructed using the method of characteristics; see, for instance Whitham [26].”
Soliton Equations and Simple Combinatorics (2008, background): “To test this idea we may try to identify soliton equations among the following family of shallow water wave equations [33]:”
Still Flowing: Approaches to Traffic Flow and Traffic Jam Modeling (2003, methodology): “In traffic, this refers to the LighthillWhitham (1955) equation (2): t +Q′ x = 0 or its integral form in Equation (1).”
Derivation of viscous Saint-Venant system for laminar shallow water (2001, background): “This derivation is classical when the viscosity is neglected (see Whitham [19], Johnson [12], Stoker [17]) but this is unsatisfactory (see Bernardi and Pironneau [4]).”
Shock detection and limiting with discontinuous Galerkin methods for hyperbolic conservation laws (2004, background): “The membrane is ruptured at time t = 0 and the solution breaks into a shock wave moving into the low-pressure gas, a rarefaction wave expanding into the high-pressure gas, and a contact surface separating the two [37].”
Stability of Standing Accretion Shocks, with an Eye toward Core-Collapse Supernovae (2002, background): “, Whitham 1974). The situation may be di erent in the case of a spherical accretion shock. The convergence of the postshock ow may amplify perturbations, and the con ned postshock volume increases the opportunity for the postshock ow to feed back on the dynamics of the shock front. For example, an a”