as on ${\bf k}$. They can be calculated by inserting the solutions  into the equations of motion but their explicit form will not be of any relevance here.

The important feature of  is that asymptotically one of the exponentials in the sum will dominate leading to a power-law evolution. In these regions, the blow-up moduli are approximately constant and the relative blow-up volumes increase until they approach values of order one where the approximation underlying our analysis breaks down. Hence, this more complicated Toda solution also conforms with our general expectation of asymptotically increasing blow-up volumes.

[**Acknowledgments**]{}\
A. L. is supported by a PPARC Advanced Fellowship, and S. M. by a PPARC Postgraduate Studentship.\

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