How is this equation solved?

by Forhad3097
Tags: field theory, mathematical physics, quantum field theory
Forhad3097 is offline
Feb1-13, 12:56 PM
P: 4
In this article, the authors present the inhomogeneous equation

$$\ddot{\phi}_2 + \phi_2 + g_2\phi_1^2 + \omega_1\ddot{\phi}_1 = 0\tag{11}$$

followed by its solution

$$\phi_2 = p_2\cos(\tau + \alpha) + q_2\sin(\tau + \alpha) + \frac{g_2}{6}p_1^2[\cos(2\tau + 2\alpha) - 3] + \frac{\omega_1}{4}p_1[2\tau\sin(\tau + \alpha) + \cos(\tau + \alpha)]\tag{14}$$

How is this solution obtained?
Phys.Org News Partner Physics news on
Physicists design quantum switches which can be activated by single photons
'Dressed' laser aimed at clouds may be key to inducing rain, lightning
Higher-order nonlinear optical processes observed using the SACLA X-ray free-electron laser
Bill_K is online now
Feb1-13, 01:09 PM
Sci Advisor
Bill_K's Avatar
P: 3,853
You left out a crucial part of the solution: φ1 = p1 cos(τ + α). Plug that into the equation and you have a driven harmonic oscillator, solved in any calc book.
Forhad3097 is offline
Feb20-13, 10:52 AM
P: 4
I have expanded the equation(9) from the paper . $$-[1+\epsilon \omega_1+ \epsilon^2 \omega_2+\epsilon^3 \omega_4...][\epsilon \ddot\phi_1+\epsilon^2 \ddot\phi_2+\epsilon^3 \ddot\phi_3....]+\epsilon^2[\epsilon \Delta\phi_1 + \epsilon^2 \Delta\phi_2+\epsilon^3 \Delta\phi_3.....]=\epsilon \phi_1+\epsilon^2 \phi_2+\epsilon^3 \phi_3.....+[g_2 \phi^2 + g_3 \phi^3....]$$
From this equation We can write equation (10), (11) and (12) and so on. but equation (12) is not matching with the expanding equation I did. I think problem in expanding with $$[g_2 \phi^2 + g_3 \phi^3....]$$.
can you please have a look, that where is the problem?

Register to reply

Related Discussions
Can this equation be solved? Calculus & Beyond Homework 3
Can this equation be solved? Calculus & Beyond Homework 5
[SOLVED] Lenses - Thin-Lens Equation and Magnification Equation Introductory Physics Homework 2
[SOLVED] differential equation Calculus & Beyond Homework 10
[SOLVED] The Dirac Equation Advanced Physics Homework 4