Nonlinear Definition and 558 Threads

Homework Statement $$y''+6y^{2/3}=0$$ Homework Equations Nothing comes to mind The Attempt at a Solution I don't really know where to start. Any tricks or tips are appreciated. This isn't a homework question, but I posted here since I didn't know where else to post. Thanks for your time

One of my friends needs to numerically solve this two dimensional boundary value problem but has now idea where to begin. Could anybody help? ## [(K H )(f g_x-gf_x)]_x+[(K H )(f g_y-gf_y)]_y=0 #### K H G^2 (f^2+g^2)+\frac 1 2 [KH (f^2+g^2)_x]_x+\frac 1 2 [K H (f^2+g^2)_y]_y-K...

1. Show that T isn't a linear transformation and provide a suitable counterexample. ##T \begin{bmatrix}x\\y \end{bmatrix} = \begin{bmatrix}x - 1 \\ y + 1 \end{bmatrix}## 2. The attempt at a solution ##\text{let}\, \vec{v} = \begin{bmatrix}0\\0 \end{bmatrix}. \text{Then,}## ##T(\vec{v}) =...

Hi all, I have a nonlinear equation of the form: \frac{TP_x}{TP_R} = c_0 + c_1 U_R^n + c_2 \frac{T_R^2}{\sqrt{U_R}} This equation describes the relationship between tidal parameters and river discharge (velocity) in tidal rivers derived from the 1-D St. Venant equations. TPx is some tidal...

Homework Statement In this problem, you will calculate the perihelion shift of Mercury simply by dimensional analysis. (a) The interactions in gravity have ##\mathcal{L}=M^{2}_{Pl}\Big(-\frac{1}{2}h_{\mu\nu}\Box...

What would be the best book for me if I want to learn nonlinear dynamics ? I have my basics clear in linear differential equations, linear system theory, integral transforms and random process if they suffice as prerequisites.

Hello every one, I have an equation related to my research. I wonder if anyone has any suggestion about solving it? y''+y' f(y)+g(y)=h(x) thanks

According to my textbook the nonlinear Schrödinger equation: $$\frac{\partial A(z,T)}{\partial z} = -i \frac{\beta_2}{2} \frac{\partial^2A}{\partial T^2} + i \gamma |A|^2 A \ \ (1)$$ can be cast in the form $$\frac{\partial U(z,\tau)}{\partial z} = -i \frac{sign \beta_2}{2} \frac{1}{L_D}...

This is actually a straightforward question, but I'm struggling to find answers because I don't know very much about lasers. I want to use a nonlinear crystal for frequency doubling in an infrared laser (1480 nm) so that the output is half @ 740 nm. I know that nonlinear crystals like KTP are...

I'm trying to find a closed form (an algebraic solution) for the following system: x² - y² = 5 x + y = xy It's a bit tricky but I manage to end up with the quartic equation: x^4 - 2x^3 + 5x^2 -10x + 5 =0 And this is where I get stuck looking for a closed form root. Any suggestion would be...

Here is the table of contents of Nonlinear Dynamics and Chaos (by Strogatz) Overview Flows on the Line Bifurcations Flows on the Circle Linear Systems Phase Plane Limit Cycles Bifurcations Revisited Lorenz Equations One-Dimensional Maps Fractals Strange Attractors Last quarter, there was a...

I need to solve the well known momentum equation in 3D cylindrical coordinates: ρ(∂v/∂t +(v.∇)v)=A where A and the velocity v are both local vector variables. I am actually looking for the stationary solution to the equation, i.e. no ∂/∂t term) I have tried evolving the velocity and tried...

Show that, in polar coordinates, the system is given by r′ = r(r^2 − 4) θ′ = 1x′1 = x1 − x2 − x1^3 x′2 = x1 + x2 − x2^3

Homework Statement The state space model of a nonlinear system is x'_1(t) = 2x^2_2(t) - 50 x'_2(t) = -x_1(t) - 3x_2(t) + u(t) Where x_1(t) and x_2(t) are the states, and u(t) is the input. The output of the system is x_2(t). Find the state space model of this system linearized at the...

I am learning nonlinear optics and recently got my hand on Nonlinear Optics by Robert W Boyd. Any other suggestions? Also is there a solution manual available for the above textbook? http://www.sciencedirect.com/science/book/9780123694706

When I point a 5 milliwatts red laser at a pile of barium borate crystals, all I get is red speckles of scattered light. When I point a 100 milliwats blue laser at the same pile of barium borate crystals, I get blue speckles. When I point a 2000 milliwats green laser at the pile of barium borate...

Hi there, I'm having a little trouble understanding the "distinguishability" of frequencies in the nonlinear electric susceptibility tensor. As far as I understand, if we have a SHG process with two collinear beams of the same polarization and frequency ω, there is only one susceptibility...

Homework Statement Evening all, I'm trying to solve the 2-D diffusion equation in a region bounded by y = m x + b, and y = -m x -b. The boundary condition makes it complicated to work with numerically, and I recall a trick that involves a coordinate transformation so that y = m x + b, and y =...

Evening all, I'm trying to solve the 2-D diffusion equation in a region bounded by y = m x + b, and y = -m x -b. The boundary condition makes it complicated to work with numerically, and I recall a trick that involves a coordinate transformation so that y = m x + b, and y = -m x -b are mapped...

Homework Statement I need to solve the follwing differential equation $$(\frac{df}{dt}) \dfrac{4 n e^{4nf(t)}-9n e^{2nf(t)} (\frac{df}{dt})^2 + e^{2nf(t)} r^2 \frac{d^2f}{dt^2}+5n (\frac{df}{dt})^4 r^4 - r^4 \frac{d^2f}{dt^2} (\frac{df}{dt})^2}{-e^{2nf(t)}+ (\frac{df}{dt})^2 r^2}=0 $$...

Recently I was a witness and a minor contributor to this thread, which more or less derailed, in spite of the efforts by @Samy_A. This is a pity and it angered me a bit, because the topic touches upon some interesting questions in elementary functional analysis. Here I would like to briefly...

5000 In each of Problems 21 through 24,determine the order of the given partial differential equation;also state whether the equation is linear or nonlinear. Partial derivatives are denoted by subscripts. 21. $u_{xx} + u_{yy} + u_{zz}= 0$ 23. $u_{xxxx} + 2u_{xxyy} + u_{yyyy} = 0$ 22. $u_{xx} +...

I have read a book that demonstrate the origin of electrical susceptibility of high order in harmonic generation: (in Robert Boyd's book : "Nonlinear optics"). For example, he show clearly for the case of second harmonic generation, how \chi^{(2)} depends on matrix element of electric dipole...

Homework Statement I have a particle moving with uniform velocity in a frame ##S##, with coordinates $$ x^\mu , \mu=0,1,2,3. $$ I need to show that the particle also has uniform velocity in a frame ## S' ##, given by $$x'^\mu=\dfrac{A_\nu^\mu x^\nu + b^\mu}{c_\nu x^\nu + d}, $$ with ##...

Good evening I have these coupled equations and was wondering if there is any chance solving them analytically. If not, how would you approach it numerically? (shown in attachment) Thank you very much

Hello. I was wondering if anyone here had come across an equation similar to this one: \alpha(uu_x)_x= u_t Any info regarding this equation or tips on how to solve this would be appreciated :) I came across these solutions: http://eqworld.ipmnet.ru/en/solutions/npde/npde1201.pdf, but how do...

Hey! I'm currently solving the heat equation using finite differences. I have a conductivity k(u) that varies greatly with temperature. It even drops to zero at u=0. I have discretized the equations the following way: \frac{\partial}{\partial x}\left( k(u) \frac{\partial u}{\partial x}\right) =...

Homework Statement 1. Maximise ##x_1^2+(x_2-5)^2## subject to ##x_1 \geq 0, x_2 \geq 0## and ##2x_1+x_2 \leq 4##. 2. Minimise ##x_1^2+(x_2-5)^2## subject to ##x_1 \geq 0, x_2 \geq 0## and ##2x_1+x_2 \leq 4##. 3. Maximise ##2x_2^2-x_1## subject to ##x_1 \geq 0, x_2 \geq 0## and ##x_1^2+x_2^2...

Hello, I'm a student in mechanical engineering and right now, we're studying non Linear Calculation of Structures. We have a project which consists on evaluating one of the solutions to stop a tourism aeroplane CESSNA 172, like a cable to stop it when it lands. So we started our study with a...

How can one tell if an equation is linear or not? Is it necessary to memorize what the graph looks like?

For the linear differential equation, it says that a_n and b_n are constants or functions of x. This implies that a function of x = f(x) = constant. How can a number be a constant if it is a function? I think I'm misunderstanding something.

Hi guys! I am trying to fit a function whose x data depends nonlinearly on the parameter of the fit and I am having hard time doing that! I will explain better: from my experiment I was able to measure my ydata e my x0 array and I know that my xdata are: x=x0+a/(1+4x^2), with a being a...

Homework Statement Consider a consumer with wealth ##w## who consumes two goods, which we shall call goods ##1## and ##2.## Let the amount of good ##\mathcal{l}## that the consumer consumes be ##x_{\mathcal{l}}## and the price of good ##\mathcal{l}## be ##p_{\mathcal{l}}##. Suppose that the...

Hi guys, I was browsing in regards to differential equations, the non-linear de and came up with this site in facebook: https://www.facebook.com/nonlinearDE Are these people for real? Can just solve any DE like that, come up with a series? Not an expert in this area, so I do not know what if...

Hi, I have a small two dimensional nonlinear objective that has a very well defined minimum and maximum. Here is the function: $$f(x,y)=2(1-x)^{2}e^{-x^{2}-(y+2)^{2}}-9(\frac{x}{5}-x^{3}-y^{5})e^{-x^{2}-y^{2}}-\frac{1}{5}e^{-(x-1)^{2}-y^{2}}$$ Attached is it's plot and contour. Notice this...

Hi. I'm a bit confused on determining whether a certain PDE is linear or non-linear. For example, for the wave equation, we have: u_{xx} + u_{yy} = 0, where a subscript denotes a partial derivative. So, my textbook says to write: $L = \frac{\partial^2}{\partial x^2} + \frac{\partial^2}{\partial...

Homework Statement The problem and its solution are attached in the TheProblemAndSolution.jpeg file. Homework Equations V = RI G = 1/R The Attempt at a Solution I tried to understand what the solution said, but I'm still very lost. Here's what I'm stuck on.: When the solution says "Since...

how do you solve this equation? y´´ + k/(y^2) = 0 ? I got it from applying Newton's 2nd law of motion to an object falling from space to Earth only affected by gravitational force. Thank you!

I have this system of equation: A = \frac{\alpha + \beta + \gamma}{3} B = \sqrt[2]{\frac{\beta \gamma + \gamma \alpha + \alpha \beta}{3}} C = \sqrt[3]{\alpha \beta \gamma} And I want to solve this system for α, β and γ. In other words, I want to express α, β and γ in terms of A, B and C...

This isn't a precise homework question, but this seemed like the most reasonable place to post. If not, please feel free to move it. I have a large set of data points that should fit to a known equation (the Drude-Smith model for conductivity) The equation the data should fit to is: σ(ω) =...

Hi guys, after hours of searching internet I couldn't find much real-life examples of second order nonlinear dynamic systems (only tons of tons of equation and system theory... got totally frustrated). They will serve as a base process for modeling controllers. So far I found propeller pendulum...

I need to find a trapping region for the next nonlinear ODE system $u'=-u+v*u^2$ $v'=b-v*u^2$ for $b>0$. What theory i need to use or which code in Mathematica o Matlab could help me to find the optimal trapping region.

Perhaps the title says it all, but I should expand it more, I guess. So I am trying to explore more about constrained optimization. I noticed that there are very little to no formal (with examples) discussions on algorithms on nonlinear constrained optimization in the internet. They would...

Hello I have a system of differntial equations: dx/ds = sin(p) dy/ds=cos(p) dp/ds = k dk/ds = -1/EI(s)*(k*dEI/ds+f*sin(p)) x(0)=y(0)=p(0)=p(L)-pl = 0 These are nonlinear differential equations. I should use some sort of nonlinear finite difference. But I do struggle to setting up the finite...

Nonlinear sigma models are particular field theories in which the fields take values in some nontrivial manifold. In the simplest cases this is equivalent to saying that the fields appearing in the lagrangian are subject to a number of constraints. Since the lagrangian fields are not independent...

What textbooks would you recommend for self studying Nonlinear Dynamics? I am a undergraduate junior who will be doing research on nonlinearity of spiking neurons. I have taken courses on ODE, vector calculus, probability, statistics, and linear algebra.

i want to solve a nonlinear PDE with finite difference method ,but using just discretization like in linear PDE , it will lead to nowhere , what's the right way to use FDM to solve nonlinear PDE or could someone provide me with book's titles or articles that can help me solving a nonlinear pdf...

Homework Statement Okay, here's the deal:I have been given a second order nonlinear differential equation, and I have also been given the general solution with constants A and B. I am supposed to find the constants A and B. The solution represents a fermion at rest, since the solution does not...

How to find matix K (Riccati equatin) <<<<<< pleas help me

Homework Statement Solve from the differential equation below numerically for the function \phi(x) for x \in [0,L] \phi '' (x) + D(x) sin(\phi (x) ) + E sin(\phi (x) ) cos( \phi (x) ) = 0 with D(x) a polynomial. Homework Equations Matlab. The Attempt at a Solution I can rewrite it in a...