Recent content by Wuberdall

Hi PF, I graduated (MSc) six months ago with a 3.7/4.0 GPA and is still unemployed. During my time at university, I focused on my studies and did not give my future work life much thought. Consequently, I do not really know what my options are as a physicist. Sure, after reading countless job...

Thank you jedishrfu, I can't seem to get access to this chapter. I believe it is my university that haven't bought the subscription to the journal Mathematics in Science and Engineering.

Hi PF, Is there someone here, who can recommend some good introductory literature on the Benjamin-Ono equation (BO)? I have skipped through the book Nonlinear PDE's for scientists and engineers by L. Debnath and in it Debnath only presents the BO equation without a thorough discussion hereof...

Thanks, for your time. I have figured it out now. It turned out that I was a bit rusty. So I found my old and dusty book by Strogatz on my bookshelf. All your comments make complete sense now and I see why they are true. I wish you a happy and sunny weekend.

Thanks, this is exactly what I was looking for and also what my intuition told me. How do you conclude that their is exactly one fixed point ?

Hi, this is not homework or course related. I am trying to determine if a fixed point for a certain dynamical system is unique. In doing so I come across the above recurrence relation. So what I am really looking for, is a solution and whether or not this solution is unique

Hi Physics Forums, I am stuck on the following nonlinear recurrence relation $$a_{n+1}a_n^2 = a_0,$$ for ##n\geq0##. Any ideas on how to defeat this innocent looking monster? I have re-edited the recurrence relation

Thanks, Each of the ##\mathrm{sinc}^n(x)## functions in the sequence are continuous. Thus IF the sequence where to converge uniformly to ##\mathbf{1}_{\{0\}}##, then ##\mathbf{1}_{\{0\}}## has to be continuous (which it is not). Consequently, the sequence...

Hi Physics Forums, I have a problem that I am unable to resolve. The sequence ##\{\mathrm{sinc}^n(x)\}_{n\in\mathbb{N}}## of positive integer powers of ##\mathrm{sinc}(x)## converges pointwise to the indicator function ##\mathbf{1}_{\{0\}}(x)##. This is trivial to prove, but I am struggling to...

I am struggling to evaluate the following, relatively easy, integral (it might be because its early on a monday morning): $$I_{jk}(a)=\int_0^a\chi_{[0,1)}(2^jx-k)\,dx,$$ where ##\chi_{[0,1)}(x)## denotes the indicator function on ##[0,1)## and ##j,k## are both integers. My idea is to rewrite the...

Hi, I'm currently studying percolation theory and here I'm stuck on the this "simple" algebraic equation ax^{n-1} - x +1 - a = 0 clearly, the trivial solution x = 1 solves it. But I'm told that x = 1 - \frac{2a(n-1)-2}{a(n-2)(n-1)} is another solution. This makes we wonder, if the equation can...

Because, \int_0^1 y^n\frac{\partial y}{\partial x}\mathrm{d}x = [y^{n+1}]_0^1 - \int_0^1 ny^{n-1}\frac{\partial y}{\partial x}\,y\,\mathrm{d}x as \int fg^\prime = fg - \int f^\prime g

Homework Statement let y(x, t) be a solution to the quasi-linear PDE \frac{\partial y}{\partial t} + y\frac{\partial y}{\partial x} = 0 with the boundary condition y(0, t) = y(1, t) = 0 show that f_n(t) = \int_0^1 y^n\,\mathrm{d}x is time invariant for all n = 1, 2, 3,... Homework EquationsThe...

Hi PF, As you may know, is the the elasticity/stiffness tensor for isotropic and homogeneous materials characterized by two independant material parameters (λ and μ) and is given by the bellow representation. C_{ijkl} = \lambda\delta_{ij}\delta_{kl} + \mu(\delta_{ik}\delta_{jl} +...

It follows directly - by some elementary algebraic manipulation - from Rydbergs formula. So start from Rydbergs formula and try to rewrite it on your desired form.