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Nonlinear coupled differential equation system - kinetics

  1. Aug 26, 2013 #1
    Dear All,

    Recently, I have measured a series of nonlinear vibrational spectra from which I would like to extract some useful information about kinetics of the exchange process occuring in the studied system.
    I need to fit my experimental data to kinetic model that is a solution of coupled differential equations of this form:
    [tex]
    \frac{\mathrm{d}x(t) }{\mathrm{d} t} = -k_1x(t)-k_2-k_3x^2(t)+k_4y(t) \\ \\
    \frac{\mathrm{d}y(t) }{\mathrm{d} t} = -k_5y(t)-k_6+k_3x^2(t)-k_4y(t)
    [/tex]
    where [tex]k_1,k_2,k_3,k_4,k_5,k_6[/tex] are constants

    Do you think that this system has got an analytic solution? What kind of method should I use to find it?
    I have tried assuming the solution to be series of hyperbolic functions but I failed to determine the expansion coefficients.

    Thank you in advance and have a nice day,

    Michael
     
  2. jcsd
  3. Aug 27, 2013 #2
    Hi !
    The system can be reduced to a second order non linear equation, which is too complicated to be solved analytically, on my opinion.
     

    Attached Files:

    Last edited: Aug 27, 2013
  4. Sep 2, 2013 #3
    Thank you very much for your reply. I will try to make use of numerical solution then.
     
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