Results 191 to 200 of about 2,627,124 (242)

Nonlinear Hyperbolic Equations

1996
Here we study nonlinear hyperbolic equations, with emphasis on quasi-linear systems arising from continuum mechanics, describing such physical phenomena as vibrating strings and membranes and the motion of a compressible fluid, such as air.
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A family of integrable nonlinear equations of hyperbolic type

Journal of Mathematical Physics, 2001
A new system of integrable nonlinear equations of hyperbolic type, obtained by a two-dimensional reduction of the anti-self-dual Yang–Mills equations, is presented. It represents a generalization of the Ernst–Weyl equation of General Relativity related to colliding neutrino and gravitational waves, as well as of the fourth order equation of Schwarzian ...
Tongas, A., Tsoubelis, D., Xenitidis, P.
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CENTERED DIFFERENCE SCHEMES FOR NONLINEAR HYPERBOLIC EQUATIONS

Journal of Hyperbolic Differential Equations, 2004
A hierarchy of centered (non-upwind) difference schemes is identified for solving hyperbolic equations. The bottom of the hierarchy is the classical Lax–Friedrichs scheme, which is the least accurate in computation, and the top of the hierarchy is the FORCE scheme, which is the optimal scheme in the family.
Chen, Gui-Qiang, Toro, Eleuterio F.
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Exact solutions of (2 + 1)‐dimensional Schrödinger's hyperbolic equation using different techniques

Numerical Methods for Partial Differential Equations, 2020
In this paper, we derive new optical soliton solutions to (2 + 1)‐dimensional Schrödinger's hyperbolic equation using extended direct algebraic method and new extended hyperbolic function method.
Hamood Ur Rehman, M. Imran, N. Ullah, A. Akgül   +3 more
semanticscholar   +1 more source

A Branching Random Evolution and a Nonlinear Hyperbolic Equation

SIAM Journal on Applied Mathematics, 1988
The author studies a branching random evolution process as considered by McKean, i.e., a particle moving at constant speed c along the real line, reversing direction as a Poisson process with parameter a, and splitting into \(j\geq 2\) ``daughter'' particles with probability \(b_ j\) \((\sum^{\infty}_{j=2}b_ j=1)\) after a random inter-splitting ...
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Feedback Control of Nonlinear Hyperbolic PDE Systems Inspired by Traffic Flow Models

IEEE Transactions on Automatic Control, 2019
This paper investigates and provides results, including feedback control, for a nonlinear, hyperbolic, one-dimensional partial differential equation (PDE) system on a bounded domain.
I. Karafyllis, N. Bekiaris-Liberis, M. Papageorgiou   +2 more
semanticscholar   +1 more source

A nonlinear hyperbolic volterra equation

1979
A mathematical model for the motion of a nonlinear one dimensional viscoelastic rod is analysed by an energy method developed by C.M. Dafermos and the author. Global existence, uniqueness, boundedness, and the decay of smooth solutions as t → ∞ are established for sufficiently smooth and "small" data.
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Solvability of Nonlinear Inverse Problem for Hyperbolic Equation

Journal of Mathematical Sciences, 2017
Summary: We consider the nonlinear inverse problem for a second order hyperbolic equation with unknown coefficient depending on the time. We establish the existence and uniqueness of regular solutions which are used for constructing a solution to the inverse problem under consideration.
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Investigations of Solutions of Nonlinear Hyperbolic Equations with a Small Nonlinearity and Applications

SIAM Journal on Mathematical Analysis, 1994
Summary: The Cauchy problem for the nonlinear hyperbolic equation \[ L_ \varepsilon u+ \varepsilon^ p N_ \varepsilon (t,x, D^ \alpha u,\;|\alpha| \leq q)= f_ \varepsilon (t,x) \] of order \(m\geq 2\), \(0\leq q\leq m-1\), is studied; \(\varepsilon\in (0,1]\) is a small parameter.
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Nonlinear resonance for quasilinear hyperbolic equation

Journal of Mathematical Physics, 1987
The purpose of this paper is to study the wave behavior of hyperbolic conservation laws with a moving source. Resonance occurs when the speed of the source is too close to one of the characteristic speeds of the system. For the nonlinear system characteristic speeds depend on the basic dependence variables and resonance gives rise to nonlinear ...
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