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Results tagged with mp.mathematical-physics
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user 9245
Mathematical methods in classical mechanics, classical and quantum field theory, quantum mechanics, statistical mechanics, condensed matter, nuclear and atomic physics.
5
votes
2
answers
802
views
Blow-up for the quasilinear heat equation $u_t= u \ u_{x x}$ or the related $w_t= \left(w_x ...
What kind of approaches can be used to study the following quasilinear parabolic pde
for a scalar function $u=u(x,t)$ ?
$$
u_t= u \ u_{x x}
$$
The physical problem where this pde comes from dictates …
- 141
4
votes
3
answers
1k
views
Imaginary exponential functional of Brownian motion
Thanks to the work by M. Yor and colleagues, much is known about the following exponential of Brownian motion:
$X= \int_0^{\infty}{\rm d}t \ e^{-t + g \ B(t)}$
where $g$ is a real scale parameter.
…
- 141
3
votes
3
answers
427
views
differential-difference three-term recursion
Trying to solve a PDE coming from the computation of some functional of Brownian motion,
I have came across the following Bessel-looking like functional recurrence:
$n^2 g_n(t) + t g_n'(t) = (t/2)(g …
- 141
1
vote
Imaginary exponential functional of Brownian motion
For those interested, we have released today an ArXiv preprint with what we were able to find: http://arxiv.org/abs/1101.1173
- 141
0
votes
differential-difference three-term recursion
Thanks but yes! Actually the problem as stated comes from the Fourier coefficients of the solution of the heat-like pde (with initial conditions $G(x,0)=1 \ \forall x$):
$t \partial_t G(x,t) - \part …
- 141
0
votes
differential-difference three-term recursion
This differential-difference three-term recursion occurs in conjunction with the study of an imaginary exponential functional of Brownian motion (another question I asked on MO). For those interested …
- 141
0
votes
Imaginary exponential functional of Brownian motion
It turns out that the above generating function pde is related to a Lax pair of Painlevé III/Sine-Gordon, at least for the parameter value g=2.
As soon as I have written this up, I'll post details
- 141