-
Dispersionless (or quasi-classical)
limits of
integrable partial differential equations (PDE)
arise in
various problems of
mathematics and
physics and...
- The
limit ϵ → 0 {\displaystyle \epsilon \rightarrow 0} is
called the
dispersionless limit. If we also ****ume that the
solutions are
independent of y as...
-
importance of the
Heaviside condition is that it
showed the
possibility of
dispersionless transmission of
telegraph signals.: 131 In some cases, the performance...
- waves) sine–Gordon
equation Dispersion (optics)
Dispersion (water waves)
Dispersionless equation Erdoğan, M. Burak; Tzirakis,
Nikolaos (2016).
Dispersive Partial...
- {W_{i}(x)}{W(x)}}\,\mathrm {d} x.}
Consider the
equation of the
forced dispersionless spring, in
suitable units: x ″ ( t ) + x ( t ) = F ( t ) . {\displaystyle...
- but at
small scales the
pressure term
dominates and the
waves become dispersionless with a
speed of 3 ⋅ v e , t h {\displaystyle {\sqrt {3}}\cdot v_{\mathrm...
- c {\displaystyle c} is a constant, not
dependent on
frequency (the
dispersionless case), then the most
general solution is p = f ( c t − x ) + g ( c t...
- scale, the
boundary value problem giving rise to
Rayleigh waves are
dispersionless. An
interesting special case is the
Poisson solid, for
which λ = μ {\displaystyle...
- The
linear wave
equation models the
displacement u of an
idealized dispersionless one-dimensional string, in
terms of
derivatives with
respect to time...
-
Parametric and "instantaneous" (i.e.
material must be
lossless and
dispersionless through the Kramers–Kronig relations)
nonlinear optical phenomena, in...
