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- W1446016686 abstract "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, ] where x and t represent dimensionless distance and time respectively, have considered the evolution when the initial data is given by [ u(x,0)=tanh ( Cx ), quad -infty<x<infty, ] for C constant. These computations suggest that kink and soliton structures develop from this initial profile and here the method of matched asymptotic coordinate expansions is used to obtain the complete large-time structure of the solution in the particular case C = 1/3. The technique is able to confirm some of the numerical predictions, but also forms a basis that could be easily extended to account for other initial conditions and other physically significant equations. Not only can the details of the relevant long-time structure be determined but rates of convergence of the solution of the initial-value problem be predicted." @default.
- W1446016686 created "2016-06-24" @default.
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- W1446016686 date "2015-06-04" @default.
- W1446016686 modified "2023-09-25" @default.
- W1446016686 title "The large-time asymptotic solution of the mKdV equation" @default.
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- W1446016686 doi "https://doi.org/10.1017/s095679251500025x" @default.
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