The differential-equations tag has no wiki summary.
1
vote
2answers
48 views
Does spatial coupling prohibit resonances due to an external source field?
The harmonic oscillator coupled to a sinodial external source
$$\tfrac{\partial^2 x(t)}{\partial t^2}+\omega_0^2 x(t)=F_0\sin(\omega_\text{ext}\ t),$$
has the solution
$$x(t)=x(0)\cos(\omega_0 t)+C ...
0
votes
2answers
105 views
Geometrical interpretation of complex eigenvectors in a system of differential equations
Let's consider a system of differential equations in the form
$$\dot{X} = M X$$
in two dimensions ($X = (x(t), y(t))$).
In the case that $M$ has real values, it is easy to give a geometric ...
2
votes
0answers
91 views
Black & Scholes and the Quantum Mechanics
I am interested in the link between the Black & Scholes equation and quantum mechanics.
I start from the Black & Scholes PDE
$$
\frac{\partial C}{\partial t} = -\frac{1}{2}\sigma^2 S^2 ...
2
votes
0answers
62 views
Is a solution to the Klein-Gordon equation homeomorphic (or even diffeomorphic) to a solution of an equation with a different covariance group?
Consider some solution $\psi(x,t)$ to the linear Klein-Gordon equation: $-\partial^2_t \psi + \nabla^2 \psi = m^2 \psi$. Up to homeomorphism, can $\psi$ serve as a solution to some other equation ...
1
vote
0answers
42 views
Solving the equation of relativistic motion
How does one solve the tensor differential equation for the relativistic motion of a partilcle of charge $e$ and mass $m$, with 4-momentum $p^a$ and electromagnetic field tensor $F_{ab}$ of a constant ...
1
vote
0answers
62 views
Chemical reaction as state transition?
When considering diffusion of chemicals, the reaction part is business of chemical kinetics, where the relevant characteristics of different substances come from collision theory together with some ...
0
votes
0answers
43 views
coordinate change differential equation polar
I noticed that v [in step (2.5)] is not the same as the terms from the first formula, even if they are related..
I tried to understand how did he reach to this ...
0
votes
0answers
47 views
Cauchy Problem in Convex Neighborhood
While reading the reference
Eric Poisson and Adam Pound and Ian Vega,The Motion of Point Particles in Curved Spacetime, available here,
there is something that I don't quite understand.
...
0
votes
0answers
56 views
deriving differential equation of a cart moved by a motor
This is homework and I'm having some trouble getting started. How do I go from whats given to the form that they ask for? Normally in something like this I would try to balance torque, but I'm not ...
