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Solitary waves and solitons in liquid films

机译:Solitary waves and solitons in liquid films

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We consider weakly dispersive and weakly nonlinear surface waves on liquid films in which longhyphen;range interaction forces are operative. As a first approximation, disturbances on both interfaces of the film can be described as a superposition of symmetrical and antisymmetrical waves even when considering nonlinearities. For small, but finite amplitudes, the antisymmetrical waves are free of nonlinearities, whereas for the symmetrical ones a Kortewegndash;de Vries equation can be derived. Depending on the particular thickness dependence of the longhyphen;range interaction forces the symmetrical disturbances lead to solitary waves with negative amplitudes (holes) or with positive amplitudes (intumescences). Taking as an example a soap film, with electrical double layer and Londonndash;van der Waals forces as interaction phenomenon, it is shown that observable solitons can be expected. It is put forward that the theory, presented here, is a contribution towards framing more sophisticated theories of liquid film (in)stability.

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