Nonlinear Definition and 558 Threads

First off, though I've been reading through these forums for a while now, this is my first post here, so let me briefly introduce myself. I'm finishing up my third year as an undergraduate in mathematics. Next year, I want to apply to grad school in math, specifically, I'd like to study...

According to this article, researchers have obtained measurements with an accuracy larger than the upper bound set by HUP. http://physicsworld.com/cws/article/news/45535 My first thought is that this is not a violation, since we are talking about a finite number of measurements, but then...

We did an experiment using the physical pendulum to measure gravitational acceleration g. A graph is shown in this link: http://i593.photobucket.com/albums/tt20/omicgavp/measuringggraph.jpg" A nonlinear (possibly chaotic) trend can be seen in our graph even though we assumed small-amplitude...

Nonlinear ODE, Howto attack... Hi, I've got a general nonlinear ODE equation that I have been solving in various situations, and I needed to make an approximate correction to -- but after the correction, an analytical solution to the new form evades me... So I am studying it, but my math...

I am participating in a reading course on nonlinear optics, which is a little difficult since I haven't had any formal education in quantum mechanics other than the standard introductory solving of Schroedinger's eqn. in 1D. Happily this course takes the semiclassical approach, in which the...

Can anyone please suggest whether I can use MATLAB ode45 for the numerical solution of the following equations? mx ̈+ c_x x ̇ + k_x x= F_x0+ μ(v_r ) (K 〖VB〗^2 y ̇/v) sgn(v_r ) my ̈+ c_y y ̇+ k_y y= F_y0+ (K 〖VB〗^2 (y/v) ̇ ) Where, m, c_x, k_x, c_y, k_y, F_x0, F_y0, K, v are known...

Homework Statement Let P2 be the vector space of real polynomials of degree less or equal than 2. Define the (nonlinear) function E : P2 to R as E(p)=integral from 0 to 1 of ((2/pi)*cos((pi*x)/2)-p(x))^2 dx where p=p(x) is a polynomial in P2. Find the point of minimun for E, i.e. find...

Hi everyone, How can I solve hydrogen atom with discrete nonlinear schrödinger equation? Could you help me with the mathematics of that, please?

Homework Statement y+4y^2=(y^(4)+x)y', IC: y(1)=1 Homework Equations ? The Attempt at a Solution Ive tried to figure out a substitution that will make this linear, and i can't seem to figure one... I am unsure of how to approach this?

Hi! I have to solve the nonlinear equations of motion in the article (16) (17) (18). I Trasform the system in a system of first order differential equations but i don't have the initial conditions. Is it possible to solve it with the ode45 MATLAB function?

[PLAIN]http://up.arab-x.com/Jan11/OGt43805.pngplese help me for my homework plese:cry:

this is the problem: x2y' = (2y2 - x2) here's what i have done so far: dy = (2y2/x2 - 1)dx (2y2/x2 - 1)dx - dy = 0 i used the substitution y = xv then found an integrating factor and got dx/x - dv/(2v2 - 2v - 1) = 0 but i am stuck at this point.. i know ln(x) + C is the first part...

Homework Statement Solve the diferential equation: dx/dt + Rx^2 + G = 0 G constant = 10^18 R constant = 10^-10 Initial conditions x(0) = 10^8Homework Equations what approach to take? The Attempt at a Solution First I try to apply bernoulli, but since in this equation I do not have a term...

Hello. Can anyone tell me what would be the best software to use for the nonlinear regression? I have an equation with two unknown parameters which I would like to find out. Equation looks something like this: f(x)=a*b*x/(1+b*x), where x and f(x) are known (several points) and I would like to...

What is the best approach for obtaining the inverse of a system of equations involving nonlinear equations? Say: 3x^2 - 2y = i x + y = j Solving for x and y in terms of i and j? Note: This is not a homework problem, just a general question.

Can anybody please suggest some references (preferably review articles or lecture notes etc, freely available online) for learning linear and nonlinear sigma models and their applications in particle physics?

Modelling a solid bed cooled by an uprising gas flow gave the following system of 1st order NONLINEAR PDEs dv/dt + f(t) * dv/dx = h*(u-v) du/dt = -h*(u-v) BC v(x=0,t) = 0 dv/dx(x=1,t)=0 IC u(x,t=0) = 1 where: u, v are temperatures function of (x,t) range [0,1]...

Hi all, I am having a hard time solving a partial second order differential equation with an imaginary part. I basically took a much bigger function with real and imaginary parts and simplified it down to this. I also know the solution to a similar equation (shown in image). Any help would...

Nonlinear 1st order ODE \frac{dH}{dt}=B-A*(H-Z)^{3/2} where: B,A and Z are known values H=f(t); H is function of t I've already solve this ODE numerically using a 4th order RK routine. But my question is, it is possible to get an analytical solution for H(t)?

I would like to perform a complicated nonlinear fit with mathematica, which involves a numerical integral in the fitted model. But i can't get it to work. If I say something like: NonlinearRegress[data, NIntegrate[f[x, p1, p2, y], {y, 0, 1}], {p1, p2}, x] it says the integrand evaluated...

Hi From Wiki (http://en.wikipedia.org/wiki/Nonlinear_optics): "Nonlinear optics (NLO) is the branch of optics that describes the behaviour of light in nonlinear media, that is, media in which the dielectric polarization P responds nonlinearly to the electric field E of the light." My...

Here is the equation I don't know how to solve: \begin{aligned} \left( {\frac{{{{\rm{d}}^2}}}{{{\rm{d}}{t^2}}} + \beta _1^2} \right){u_1} = {g_1}u_2^{}{u_3} \\ \left( {\frac{{{{\rm{d}}^2}}}{{{\rm{d}}{t^2}}} + \beta _2^2} \right){u_2} = {g_2}u_1^{}{u_3} \\ \left(...

Homework Statement y''+4\left(y'\right)^{2}+8=0 Homework Equations u=y'? The Attempt at a Solution I don't really know where to start, do I use u=y' substituted? So, y''=u*(du/dy)? That leads to u\frac{du}{dy}+4u^{2}+8=0 I don't think this is correct, since it leads to...

Homework Statement y'(t) = (y-5t)/(y+t) IVP: y(1)=0 Homework Equations M(x,y)dx+N(x,y)dy = 0 - or do i use - y'+p(x)y=q(x) The Attempt at a Solution Well I used the first equation (with M and N): 1. first checked that it was exact, by taking the partial of M and N with respect to y and t...

Can anyone help with the following: dy/dx = ay / (bx2 +xy ) a,b constants thanks,

High I am working on the geometrically nonlinear finite element method. I now that in this method, the internal forces on each node must be equal to external forces. How can I calculate internal forces?

Hi. I'm not even sure if I'm posting this in the best forum! I'm having a lot of trouble grasping parts of this paper.. Eur Biophys J. 2009 Jun;38(5):637-47. Epub 2009 Mar 4. A nonlinear model of ionic wave propagation along microtubules. Specifically, they use a phase space plot that...

From a textbook - The reason why the polarization plays a key role in the description of nonlinear optical phenomena is that a time-varying polarization can act as the source of new components of the electromagnetic field... the wave equation in nonlinear optical media often has the form...

Nonlinear DE (with e^t) ? Good day forum, I have this wonderful DE : dx/dt = [a - f '(t)]x + (b + d(c^t))(x^2) - 1 with, t \in [s,T] x(T) = 0 a, b, d & c are constants. f(t) = g + h(k^t) , where g, h & k are constants (but I think specifying this is of no...

Hi All - I am trying to immerse myself in NLO and purchased Robert W. Boyd's Third Edition on Nonlinear Optics. I'm already struggling just 3 pages into the book. We are looking at the polarization of a material in a NLO chromophore, so: P(t)=\epsilon [X(1)E(t)+X(2)E2(t)+X(3)E3(t)...]...

Hello everybody, could you please direct me how to solve this nonlinear differential equation analytically, so by mathematica or matlab? I really need to solve it for my research project, so please help me du/dx=d/dx[a*u^(-1/2)*du/dx]-n*u^(3/2)*(u-c)/b boundry conditions are: u(0)=b+c...

How to detect redundant equation from a system of nonlinear equation? It means how to find out a system of nonlinear equation is "linear independence"? One equation from the system can not be represented by the others in the system of nonlinear equation.

Hello guys, I am not good in advance mathematics. I have system of nonlinear equation and I want to solve it analytically, but I face some difficulties. Homework Statement The system is : (a-b)y^2-exy^2-2fx=-c 2fx^2-2cx-2fy^2=-d Homework Equations where: a,b,c,d,e,and f...

-f''-(2/x)f'+(2/x^2)f+f^3-f=0 the boundary condition is f(x=0)=0 and f(x=\infty)=1 how to solve f numerically?

Hello everybody. I have a quick question. I have the following system of nonlinear differential equations: (di/dt)(x)+(x^2 - dx/dt)(i)+ v(t) =0 _ _ _1 dv/dt = i/C _ _ _2 I know my Initial Conditions: i(0) = 0, di(0)/dt = 0, x(0) = L, dx(0)/dt = 0, v(0)=V PS- x is displacement, t is time, i...

Homework Statement y' + Ay2 = B A & B are constants and y is a function of x Find the general solution to the differential equation. (Find y(x)). Homework Equations The Attempt at a Solution This differential equation came up when I was trying to solve a problem in...

I derived an equation describing the free surface of an electrified fluid. I am currently seeking traveling wave solutions for this problem, the equation I am looking at is (1-F) f+\frac{1}{90}h^{4}f^{(4)}+\frac{3}{4h}f^{2}-\frac{1}{2}\Bigg( B-\frac{1}{3}\Bigg)...

I have been working on the problem of electrified fluid flow down a channel with a moving pressure distribution. I have derived an equation which describes the free surface of said fluid flow which is a Benjamin-Ono like equation. I have a numerical solution for this equation and it gives the...

First order nonlinear ODE -- Integrating factor + exact differentials, or not? Hello everyone, (I apologize if this did not format properly, if not I will attempt to edit it if that functionality is available upon submitting a question). I recently came across the following nonlinear ODE...

Hello, Can you give some suggestions to solve the following system of 1st order nonlinear differential equations? Thank you. \[ \begin{array}{l} u'(t) = Au^2 (t) + B(t)u + C(t) \\ u(t) = \left[ {\begin{array}{*{20}c} {x_1 (t)} \\ {x_2 (t)} \\ \end{array}} \right] \\ A = \left[...

Given the ODE system: v' = u(u2-1) u' = v-u Define w=u2+v2. Compute w'. Find the largest radius R for which u2+v2<R so that the if the solution curve (u,v) is inside that circle the solution tends to (0,0) as t--> +\infty Any guidance would be appriciated !

Dear Everyone, I am working on a physics problem of exciton diffusion involved in organic optoelectronics. It is in the form of y''+a*y+b*y^2=0. Is there a general solution to this equation? Thanks! elfine

What conditions are necessary to use the constitutive relations for Maxwell's equations? I am working in a nonlinear media, but am a little confused about whether I can assume isotropy or not. If I am assuming the media is nonlinear is it necessarily anisotropic? Or, is it possible to have...

I have the following equation to solve: u_{tt}=12{u_x}^2+12u_{xx}+{u_x}^4+6u_{xx}{u_x}^2+4u_{xxx}u_x+3{u_{xx}}^2+u_{xxxx} I have been told to look into FDM or FEM. My question, is it possible to code something in MATLAB to solve this and if so what is the best method to use and how do I do...

second order nonlinear ODE -- not autonomous This equation has arisen from a steady state problem of diffusion with nonlinear reaction: (dependent var=c; independent variable=x) c'' = ko + k1 c + k2 c^2 + k3 c x ko, etc are constants. I can obtain a solution if I drop the last term...

Hey guys I'm completing an experiment and I'm required to extrapolate data by performing nonlinear curve fitting. I have 3 sets of data: (x1, y1); (x2, y2); (x3, y3). I'm required to fit the above mentioned sets of data to the following equation ...

Maybe I'm just dumb... y'(t)=y(t)^3+f(t) find y(t) Thanks...

How, if possible, could I solve the equation: x''x=((x')^2)/2? Thanks.

In class, my teacher gave the following equations as examples of linear and nonlinear ODE. In the first equation, there are x's in front of some of the y's yet it is linear. In the second equation, there is an x in front of y^2 yet it is nonlinear - why? Also, why is the final equation...

So I thought I would try to figure out the maximum distance of our 7.62x54 round. obviously I used F=ma and for resistance I used Fdrag=(mass of bullet*density of air*v^2)/ballistic constant. the v^2 terms makes the equation nonlinear and not exactly solvable right? also, the angle at which...