Geodesic
Traveling-wave solution to a nonlinear equation in semiconductors with strong spatial dispersion
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 48 (2008) no. 5, pp. 808-812 
A. B. Alshin; M. O. Korpusov; E. V. Yushkov. Traveling-wave solution to a nonlinear equation in semiconductors with strong spatial dispersion. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 48 (2008) no. 5, pp. 808-812. http://geodesic.mathdoc.fr/item/ZVMMF_2008_48_5_a5/
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     author = {A. B. Alshin and M. O. Korpusov and E. V. Yushkov},
     title = {Traveling-wave solution to a~nonlinear equation in semiconductors with strong spatial dispersion},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {808--812},
     year = {2008},
     volume = {48},
     number = {5},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2008_48_5_a5/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

The third-order nonlinear differential equation $(u_{xx}-u)_t+u_{xxx}+uu_x=0$ is analyzed and compared with the Korteweg–de Vries equation $u_t+u_{xxx}-6uu_x=0$. Some integrals of motion for this equation are presented. The conditions are established under which a traveling wave is a solution to this equation.

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