Compactification of patterns by a singular convection or stress |
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Authors: | Rosenau Philip |
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Affiliation: | School of Mathematical Sciences, Tel Aviv University, Tel Aviv 69978, Israel. rosenau@post.tau.ac.il |
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Abstract: | A wide variety of propagating disturbances in physical systems are described by equations whose solutions lack a sharp propagating front. We demonstrate that presence of particular nonlinearities may induce such fronts. To exemplify this idea, we study both dissipative u_{t}+ partial differential_{x}f(u)=u_{xx} and dispersive u_{t}+ partial differential_{x}f(u)+u_{xxx}=0 patterns, and show that a weakly singular convection f(u)=-u;{alpha}+u;{m}, 0
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