Two-Component RD system

In this section we show how to compute the front velocity for a reaction-diffusion system of two components. The calculations can be extended easily to three or more components. Define = Yi and Y2 = Y2 for simplicity. Consider the system 

For simplicity we suppose that the initial conditions for (4.121) have the form 

To ensure the positivity of Ai and Aj, we need to choose the largest eigenvalue H(p), i.e., the largest solution of equation (4.127), 

The front velocity can be determined from (4.128) and (4.47). One of the exercises below deals with a particular case where an analytical solution for the front velocity can be obtained. 

1 Find exact solutions for the RD equation with the reaction term F p) = 

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