A NOTE ON THE INTERACTION BETWEEN SOLITARY WAVES IN A SINGULARLY-PERTURBED KORTEWEG-DEVRIES EQUATION

For the fifth-order Korteweg-de Vries equation with a small parameter multiplying the highest-derivative term it is known that solitary waves are non-local, and are accompanied by co-propagating oscillatory waves of small amplitude and short wavelength. Here we report on some preliminary results for mutual interactions of these waves. First we impose a quantization condition upon a chain of solitary waves to obtain a periodic solution. Then we compute the interaction force between two neighbouring waves and hence estimate the conditions for a bound state to occur.