Nonlinear modulation near the Lighthill instability threshold in 2+1 Whitham theory
نویسندگان
چکیده
منابع مشابه
Nonlinear modulation near the Lighthill instability threshold in 2+1 Whitham theory.
The dispersionless Whitham modulation equations in 2+1 (two space dimensions and time) are reviewed and the instabilities identified. The modulation theory is then reformulated, near the Lighthill instability threshold, with a slow phase, moving frame and different scalings. The resulting nonlinear phase modulation equation near the Lighthill surfaces is a geometric form of the 2+1 two-way Bous...
متن کاملWhitham modulation theory for the Kadomtsev- Petviashvili equation.
The genus-1 Kadomtsev-Petviashvili (KP)-Whitham system is derived for both variants of the KP equation; namely the KPI and KPII equations. The basic properties of the KP-Whitham system, including symmetries, exact reductions and its possible complete integrability, together with the appropriate generalization of the one-dimensional Riemann problem for the Korteweg-de Vries equation are discusse...
متن کاملNonlinear dynamics of higher-order solitons near the oscillatory instability threshold.
Nonlinear theory describing the dynamics of solitons in the vicinity of oscillatory instability threshold with a low frequency offset is developed. The theory is tested on the example of parametric degenerate four-wave mixing. All major predictions of our theory are in agreement with the results of direct numerical modeling. This includes the position of oscillatory instability threshold, insta...
متن کاملModulation of nonlinear waves near the marginal state of instability in fluid-filled elastic tubes
Using the nonlinear differential equations governing the motion of a fluid-filled and prestressed long thin elastic tube, the propagation of nonlinear waves near the marginal state is examined through the use of reductive perturbation method. It is shown that the amplitude modulation near the marginal state is governed by a generalized nonlinear Schr€ odinger (GNLS) equation. Some exact solutio...
متن کاملAntidiffusive and Random-Sampling Lagrangian-Remap Schemes for the Multiclass Lighthill-Whitham-Richards Traffic Model
The multiclass Lighthill-Whitham-Richards (MCLWR) traffic model, which distinguishes N classes of drivers differing in preferential velocity, gives rise to a system of N strongly coupled, nonlinear first-order conservation laws for the local car densities as a function of distance and time.We propose a new class of anti-diffusive schemes by splitting the system of conservation laws into two dif...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
سال: 2018
ISSN: 1364-503X,1471-2962
DOI: 10.1098/rsta.2017.0194