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Published online by Cambridge University Press: 04 June 2015
In this paper, an initial-value problem for the modified Korteweg-de Vries (mKdV) equation is addressed. Previous numerical simulations of the solution of\[u_{t} - 6u^{2} u_{x}+u_{xxx}=0, \quad -\infty<x<\infty, \quad t>0,\]
\[u(x,0)=\tanh ( Cx ), \quad -\infty<x<\infty,\]