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 Cet article a éte moissonné depuis la source Math-Net.Ru

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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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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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