Nonlinear Definition and 558 Threads

So I'm supposed to prove that {x}^{.}(t) = x^{2}+ t^{2} with x(0) = 0 blows up before t = 1 . I'm not sure what method to use to solve I've tried setting up an integral such as \int^{x(t)}_{x(0)} \frac{dx}{x^{2}+t^{2}} = \int^{t}_{0} dt but I didn't think I could do this since 't' is...

greetings . i cam across this problem in a research paper I'm writing . x_1+x_2+...+x_m=k_1 x^2_1+x^2_2+...+x^2_m=k_2 ...... ...... x^m_1+x^m_2+...+x^m_m=k_m k_j are constants in compact form : \sum^{m}_{i=1}x^{n}_{i}=k_{n}, n=1,2...m is there a general solution(or...

My school opened a new class this semester (Labeled as "Lasers and applications", but the syllabus has it as "Nonlinear optics and Ultrafast physics"), and I figured that as a junior-level physics major I should've been able to take it, since the course itself doesn't list any prerequisites...

Hi, all Would you guys recommend some books on the subject of nonlinear physics? And how is the recent progress about it and its related fields? Thanks!

Hi, I have a set of vectors that I would like to solve for in a nonlinear system of equations. I have tried to use scipy.fsolve to solve the system, but without success. I believe the problem is that scipy expects the same number of inputs as outputs. I have a 12x1 input vector, but I can...

Hi, I want to solve a differential equation but I have never dealt with nonlinear equations before. Here it is : A - B/x = x" for x(t) A,B are constants you can absorb the negative if it matters. I would like an analogical answer, but I'm not sure if it's possible. And any...

Homework Statement Solve the following ODE: du/dx=u^2+1 Homework Equations The Attempt at a Solution I have tried making the substitution: u^2=v but this doesn't help. Any hints will be very much appreciated

I'm trying to solve a third-order nonlinear ordinary differential equation. I couldn't get the answer even using Mathematica. The equation is: u'''(t) + u/2 u''(t) = 0 with conditions u(0)=0, u'(0)=0, u(10)=1. I need to get both analytic solution and numerical solution. For the...

Hello I want to resolve a nonlinear partial differential equation of second order with finite difference method in matlab. the equation is in the pdf file attached. Thanks

Hel(lo, p) I hope you're doing fine I'm stuck with the following: y'' = -1/(y^2) I tried guessing functions (exponentials, roots, trigs... ) , but none worked, I haven't had any DE course, so I don't have specific steps to employ, I appreciate your help, Thanks in advance

Homework Statement Find an integer x that is a solution (only need one solution, not all solutions). If no solution exists, prove that no solution can exist. 13x = 13 mod 50032 , with x > 1. Note that 5003 is prime. Here, = means "congruent to" Homework Equations Not sure. I can solve...

I have derived a first order nonlinear PDE with its corresponding initial and boundary conditions given by: dv/dt + A*(v^2)*dv/dx = 0 (where A is a constant) v(t = 0) = C (constant value) v(x = 0) = 0 I'm not quite sure how to solve this. I was thinking about using the method of...

The complete question I've been given: The Rossler equations are formally defined as dx/dt=−y−z dy/dt=x+ay dz/dt=b+z(x−c). Let us suppose that a=0.2, b=0.2, c=5.7, x(0)=y(0)=z(0)=0, t∈[0,400]. Let v1(t) be the solution to the given initial value problem, and let v2(t) be the solution of the...

is there a gas which its volume increases nonlinearly with decrease in pressure?

In physics we're told often that there is no analytical way to solve most nonlinear differential equations (I don't know if this can be proven or not, or it's just assumed because no one has found a way to do it), so we use a computer to solve them numerically. I'm wondering though, assuming...

Hi! I'm working with my PhD thesis at the moment, and I've stumbled upon a pretty involved problem. What I have is a system of equations like this: \frac{dx}{dt} = A \cos(z) \frac{dy}{dt} = B x \frac{dx}{dt} \frac{dz}{dt} = y where A and B are constants. I also have a stochastic term to z...

Homework Statement Find the fixed points and classify them using linear analysis. Then sketch the nullclines, the vector field, and a plausible phase portrait. dx/dt = x(x-y), dy/dt = y(2x-y) Homework Equations The Attempt at a Solution f1(x,y) = x(x-y) x-nullcline: x(x-y) = 0 \Rightarrow...

Hello, Does anyone know of a nonlinear 2nd order DE which must be solved numerically? I've got a new idea about how tackle it analytically... So I need one with a known solution to check my results.thanks!

hi,I want to solve this problem g=(2*k-1)*y^(k-1)-((1-y^(k-1))/(1-y)); with different k and compute real and positive y so I wrote this problem in MATLAB : clear clc syms y k g=(2*k-1)*y^(k-1)-((1-y^(k-1))/(1-y)); s=input('k='); r=subs(g,k,s); d=solve(r,y) for...

Homework Statement m*dv/dt = - mg - kv^2, where m,g and k are constants and v(t) is what I should solve Homework Equations The Attempt at a Solution At first I solved homogeneous equation m*dvh/dt = -kvh^2 and got vh = m/(kt - cm). Where c is also constant. Then I treid to...

Homework Statement A certain op amp has a maximum output voltage range of ±9 V. The maximum output current magnitude is 20 mA. The slew-rate limit is SR = 300 kV/s. The op amp is used in the amplifier circuit, shown in the diagram below. For a frequency of 10 kHz and RL = 2.2 kΩ, what peak...

Homework Statement Find the orthogonal trajectories of the given families of curves. x^2 + y^2+2Cy=1 Homework Equations The book has covered homogeneous and separable methods.The Attempt at a Solution To find the orthogonal trajectories, we simply find the curves whose tangents are...

Please teach me this: I hear that linear sigma model has application in pion,nuclear physics.But do not understand what is the application of nonlinear sigma model in QFT? Thank you very much in advance.

I was trying to solve a calculus problem (about the equation of the curve traced by a dog chasing a postman) and I came across the following equation. I would like to know how to solve it. \frac{w}{v}(1-\frac{y(x)y''(x)}{{y'(x)}^{2}})=\sqrt{1+{y(x)}^{2}}-\sqrt{1+{C}^{2}} Thanks.

I need to derive the solution for the differential equation analytically: y'' + g(t,y(t)) = 0 y'(0) = z_o y(0) = y_o I know the solution is: y(t) = y_o + z_ot - single integral from 0 to t of (t-s)g(s,y(s))ds I believe I need to assume something about the solution being a function...

Hi there, I've having problems solving a particular nonlinear ODE. Any help/suggestions will be highly appreciated. The nonlinear ODE is: v[t]*v'[t] + (4*v[t])/(t^2 - 1) = t/(t^2 - 1) Thank you.

Please teach me this: In QTF theory book of Schoeder say: In nonlinear sigma model L=\intdx\frac{1}{2g^{2}}(\delta _{\mu}n^{\rightarrow})(consider2<d<4 where d is the dimension number of spacetime).If we consider the Lagrangian as the Boltzman weight of a partition function,then the...

I'm doing my economics thesis on game theory, and need to solve a system of nonlinear equations (these will be the reaction functions). Unfortunately, I have no idea how to solve it explicitly--indeed, I am a bit worried its impossible with the parameters. It is rather symmetric though. The...

Hi All, I have been trying to solve following nonlinear differential equation, but I couldn't solve it. 0 = a*[f(t)]^{z/(z-1)} + (-t+C)*f(t) + b*[df(t)/dt] where a, b and C are constants and 0< z<1. Could you please help me how to solve this nonlinear differential equation? I would...

Please teach me this: In linear and nonlinear sigma model, the spontaneous symmetry broken is inevitable happened or it may be happened and it may be not happened?Because the expectation value of field may be zero or may be not zero,then it seem that sometimes the hidden symmetry broken not...

Is there any good arguments or reasons for why it seems the general consensus is that the linear Schroedinger equations is fundamental? I know that if it turns out either of these are nonlinear it would falsify certain readings of QM so it would be interesting if there is indeed no real good...

I've been trying to solve this one for a while. My professor wasn't even sure how to do it. Any suggestions? y''+t*y+y*y'=sin(t)

Hello All, I'm working with a microcontroller and want to take analog measurements using its built-in ADC. However, I want to be able to measure voltages much higher than just 0-5V. My *seemingly* simple solution to this was to grab a 500k 25-turn potentiometer which I could connect up as a...

Hi, what are some good textbooks dedicated to this subject? I have a short time to learn everything about this subject (upto a certain level). I'm trying to fit a non-analytic curve (whose form I know) to some data. edit- sorry, I don't only mean non-linear, I mean non-analytic. The curve is...

Hi, I have some equations I have derived though energy balances and have been using the Integration Factors method to solve equations in the form: dy/dx + Py = Q However, my original equations only work if I assume some variables to be constants. Removing this assumption leaves me with...

Hello, I'm trying to (numerically) solve the equation y''*y=-0.5*y'^2 in Mathematica. I know there's an analytic solution (and I know how to calculate it), but I want to modify this equation and thus need to verify that the numerical solution for the original equation is exact. I'm using...

Hi everyone, I am studying a 2-D nonlinear dynamics system, with two key parameters. But I have trouble when I want to locate where the homoclinic bifurcation occurs in the parameter space. Can anyone give me some ideas or reference readings? Thx

y^2=y' \Rightarrow y=\frac{y'}{y} \Rightarrow \int y dx = ln \left( y \right) \Rightarrow y=e^{\int y dx}=e^{\int e^{\int y dx} dx}=e^{\int e^{\int e^{\int y dx} dx} dx}=\cdots Is that correct?

While solving a problem involving equilibrium positions of charges on a line, I came up with a recurrence relation which is nonlinear, and moreover implicitly defined. Here it is: x_{0}=0 and \sum^{n-1}_{i=0} \frac{1}{(x_{n}-x_{i})^{2}} = 1. I should also mention that 0 \leq x_{n}< x_{n+1} for...

Hi all, I have more or less convinced myself through trial and error that the following three-dimensional non-linear simultaneous equation cannot be solved. However, it would be great if someone could provide me with a proper mathematical reason as to why this is not solvable, rather than me...

Hello, everyone There is a control theory problem that i would like to ask for help here. Suppose a very simple nonlinear system as follows x' = u y = (2-cosx)*(2-cosx) how to find a control law u that makes the output y can track a constant asymptotically, of course the x should...

For a general dynamic system: dXi/dt = Fi(X1, X2,...,Xn), i=1,...,n, Q.1 do you have some ideas of the existence conditions of following PDE: a) (grad U, grad U + F) = 0 in n-dimension domain, (,) is inner product; b) U >=0 Does it need a first type or second type of boundary...

Hello, I've started learning how to numerically integrate ODE's and I've run aground when i posed a 2nd order system for mathematica. Here is my initial code: NDSolve = [{x'[t] == -y[t] - x[t]^2, y'[t]==x[t], x[0]==1, y[0]==0.5},{x,y},{t,0,30}] and i get an error message saying the...

Homework Statement dv/dt = (k+v2)/h Homework Equations k is a constant, and v and h are variables where h is independent of v but v is dependent of h (v is a function of h and t). The Attempt at a Solution dv/(k+v^2) = dt/h. The problem I have is with dealing with the right side...

I have been deriving a formula from physics. Anyway, I came across a equation that goes by the form y = exp(1/(xy)) *(b - 1/x) solve for y ; b is a constant there are other constants but i removed them for simplicity. or x = exp(1/x) solve for x , it is a function Could some one at least...

Homework Statement The following equation turned up while I was trying to make an integral stationary in a 'calculus of variations' problem. y^{\prime}(x)^2 + 1 = y^{\prime\prime}(x) y(x) How would one go about solving this nonlinear equation?

I am trying to solve the following system of 2n variables: w1 + w2 + ... + wn = b0 w1x1 + w2x2 + ... + wnxn = b1 w1x12 + w2x22 + ... + wnxn2 = b2 ... w1x12n-1 + w2x22n-1 + ... + wnxn2n-1 = b2n-1 for w1, w2 ... wn and x1, x2 ... xn. The problem is the using the Solve command returns...

\frac{d\mu }{dt}=-\left( kx\right) \left( \frac{\mu _{m}^{3}-\mu ^{2}\mu _{m}}{\mu ^{2}+\mu _{m}^{2}-2\mu \mu _{m}+\mu ^{2}K_{s}}\right) \frac{dx}{dt}=\mu x Any method for me to solve the pair of nonlinear equations or numerical graph of the differential equation. *\mu_{m} and K_{s} are...

Homework Statement I'm given two equations first (d^2)*r/dt^2 - r((d*theta/dt)^2)= (-A)/r^2 --- this is a non linear second order differential equation second (r^2)*((d*theta)/dt)=B B and A are...

How should I go about solving this problem? This is only to get a better understanding of how NLLS works. F(x;a) = (1+a1*x)/(a2+a3*x) (so n = 3) I am choosing a1,a2,a3 to be 2,3,5 respectively. I am also picking 6 data points (so m = 6): (0, 0), (-1/4, 1/4), (-1/2, 1/10), (1/4, 1/4)...