The Whitham principle for multikink solutions of reaction-diffusion equations
نویسندگان
چکیده
An useful strategy for the study of nonlinear partial differential equations (PDE) arising in pattern formation is to consider asymptotic solutions containing one or several localized defects and to simplify the dynamics by finding the equations of motion of the system of interacting defects. The great advantage of this approach is that we are dealing with ordinary differential equations (ODEs) instead PDEs. This type of approach has been successfully applied to solitons in continuous and discrete sine-Gordon equation [16, 17, 10, 13, 12], Á classical field theory [14], Korteweg-de Vries equation [11], non-linear Schrödinger, Klein-Gordon [11, 8, 9], and Frenkel-Kontorova [2] lattices, Fisher-KolmogorovPetrovsky-Piscounoff (FKPP) equation [5], to bubbles in Cahn-Hilliard equation [3].
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