This article is cited in 11 papers

Traveling-wave solution to a nonlinear equation in semiconductors with strong spatial dispersion

A. B. Alshin, M. O. Korpusov, E. V. Yushkov

Faculty of Physics, Moscow State University, Leninskie gory, Moscow, 119992, Russia

Abstract: 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.

Key words: nonlinear Korteweg–de Vries equation, traveling-wave solutions, semiconductors with strong spatial dispersion.

UDC: 519.634

Received: 29.10.2007

 English version: Computational Mathematics and Mathematical Physics, 2008, 48:5, 764–768

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