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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2010, Volume 50, Number 7, Pages 1276–1284 (Mi zvmmf4908)  
Breather collapse for a dispersive effective equation: asymptotics on the well-posedness boundary

S. I. Serdyukova

Joint Institute for Nuclear Research, Dubna, Moscow oblast, 141980 Russia
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Abstract: 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.
Key words: wave processes in periodic stratified media, nonstandard linear partial differential equations, Cauchy problem with discontinuous initial data, asymptotics of solutions at large $t$, saddle point method, stationary phase method, finite-difference method, matrix tridiagonal Gaussian elimination, stability, analytical computation system REDUCE.
Received: 02.11.2009
English version:
Computational Mathematics and Mathematical Physics, 2010, Volume 50, Issue 7, Pages 1212–1220
DOI: https://doi.org/10.1134/S0965542510070109
Bibliographic databases:
Document Type: Article
UDC: 519.634
Language: Russian
Citation: S. I. Serdyukova, “Breather collapse for a dispersive effective equation: asymptotics on the well-posedness boundary”, Zh. Vychisl. Mat. Mat. Fiz., 50:7 (2010), 1276–1284; Comput. Math. Math. Phys., 50:7 (2010), 1212–1220
Citation in format AMSBIB
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