Geodesic
Breather collapse for a dispersive effective equation: asymptotics on the well-posedness boundary
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 50 (2010) no. 7, pp. 1276-1284

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For the solution of the Cauchy problem for the equation $$ u_{tt}=u_{xx}+i2u_{ttx}+u_{ttxx} $$ with discontinuous initial data, asymptotic formulas as $t\to\infty$ are derived, which agree well with numerical results. The stability of the numerical methods used is analyzed. Other results are presented concerning nonstandard linear equations produced by homogenizing the equations describing wave processes in periodic stratified media. 
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     author = {S. I. Serdyukova},
     title = {Breather collapse for a dispersive effective equation: asymptotics on the well-posedness boundary},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1276--1284},
     publisher = {mathdoc},
     volume = {50},
     number = {7},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2010_50_7_a9/}
}
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S. I. Serdyukova. Breather collapse for a dispersive effective equation: asymptotics on the well-posedness boundary. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 50 (2010) no. 7, pp. 1276-1284. http://geodesic.mathdoc.fr/item/ZVMMF_2010_50_7_a9/