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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

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# Nonlinear coupled differential equation system - kinetics

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