Shock and traveling wave phenomena on an externally damped, non-linear string |
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Authors: | Ivan Christov |
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Institution: | a Department of Engineering Sciences and Applied Mathematics, Northwestern University, Evanston, IL 60208, USA b Code 7181, Naval Research Laboratory, Stennis Space Center, MS 39529, USA |
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Abstract: | We examine the propagation of shocks and traveling wave phenomena on a one-dimensional string that is executing finite-amplitude, transverse vibrations in a resisting medium. As part of our study, we develop an approach that allows us to describe, albeit approximately, the evolution and propagation of a shock front using analytical methods. In addition, exact traveling wave solutions, one of which involves the Lambert W-function, of the string's equation of motion are determined and analyzed. Lastly, a possible new form of the solution to the linearized problem is presented and extensions and other applications of the present work are briefly discussed. |
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Keywords: | Non-linear string Shock wave MUSCL-Hancock scheme Traveling wave solution Lambert _method=retrieve& _eid=1-s2 0-S0020746208002242& _mathId=si31 gif& _pii=S0020746208002242& _issn=00207462& _acct=C000054348& _version=1& _userid=3837164& md5=0225da0996ef4da8e1178a91a647906b')" style="cursor:pointer W-function" target="_blank">" alt="Click to view the MathML source" title="Click to view the MathML source">W-function |
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