Geodesic
Local solvability and solution blow-up of one-dimensional equations of the~Yajima--Oikawa--Satsuma type
Teoretičeskaâ i matematičeskaâ fizika, Tome 193 (2017) no. 2, pp. 179-192

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We consider one-dimensional equations of the type of the Yajima–Oikawa–Satsuma ion acoustic wave equation and prove the local solvability. Using the test function method, we obtain sufficient conditions for solution blow-up and estimate the blow-up time.
Keywords: blow-up, local solvability, ion acoustic wave. 
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     author = {A. A. Panin and G. I. Shlyapugin},
     title = {Local solvability and solution blow-up of one-dimensional equations of {the~Yajima--Oikawa--Satsuma} type},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {179--192},
     publisher = {mathdoc},
     volume = {193},
     number = {2},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2017_193_2_a0/}
}
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A. A. Panin; G. I. Shlyapugin. Local solvability and solution blow-up of one-dimensional equations of the~Yajima--Oikawa--Satsuma type. Teoretičeskaâ i matematičeskaâ fizika, Tome 193 (2017) no. 2, pp. 179-192. http://geodesic.mathdoc.fr/item/TMF_2017_193_2_a0/