Among his topics are solid continuum mechanics, the finite element method, the wave equation
for solids, the simulation of strong ground motion, elasto-plasticity and fracture mechanics, the analysis of faulting, the simulation of faulting with the boundary element method, multi-agent simulation for evacuation process analysis, high performance computing application, and meta-modeling theory for the construction of numerical analysis models.
(1) The aether hypothesis was introduced and became popular in the nineteenth century when new optical experiments suggested describing the propagation of light by a wave equation
. Aether was thought to be the universal medium in which the light waves oscillate.
In this study, FWISIMAT is developed in both time and frequency domain based on acoustic wave equation
. The frequency-domain inversion approach is equivalent to the time-domain inversion approach if all of the frequency data components are used in the inversion process (Hu et al., 2009).
Indeed, the enforcement of the wave equation
for the electric field in conjunction with the divergence-free condition, may enter in conflict with boundary conditions in a very wide range of circumstances.
As a further step, the first author proved the generalized Hyers-Ulam stability of the wave equation
without source (see [16,17]).
and then the scalar wave equation
in terms of u can be expressed by
In "Nonlinear Green's Functions for Wave Equation
with Quadratic and Hyperbolic Potentials," the author A.
Using tortoise coordinate transformation, Klein-Gordon equation, Maxwell's electromagnetic field equations, and Dirac particles can be transformed into single form of wave equation
near the event horizon.
It can be shown that if the displacement u satisfies (8) of Hamilton's principle, then it must also satisfy a differential wave equation
under certain conditions.
In the article titled "On a Nonlinear Wave Equation
Associated with Dirichlet Conditions: Solvability and Asymptotic Expansion of Solutions in Many Small Parameters" , there are similarities with two of the authors' previous publications; one of them was cited:
There is also an important paper on finding exact solution of nonlinear sixth-order solitary wave equation
using the improved generalized tanh-coth method.
One of the major roles of nonlinear partial differential equations is the study of nonlinear wave equations
. For example, the Benjamin-Bona-Mahony equation is a nonlinear wave equation
, which is also known as the regularized long wave equations