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International Journal of Theoretical Physics

, Volume 37, Issue 5, pp 1547–1567 | Cite as

Exact Traveling-Wave Solutions to Bidirectional Wave Equations

  • Min Chen
Article

Abstract

In this paper, we present several systematicways to find exact traveling-wave solutions of thesystems
$$\eta _t + u_x + \left( {u\eta } \right)_x + au_{xxx} - b\eta _{xxt} = 0$$
$$u_t + \eta _x + uu_x + c\eta _{xxx} + du_{xxt} = 0$$
where a, b, c, and d are real constants. These systems,derived by Bona, Saut and Toland for describingsmall-amplitude long waves in a water channel, areformally equivalent to the classical Boussinesq systemand correct through first order with regard to asmall parameter characterizing the typicalamplitude-todepth ratio. Exact solutions for a largeclass of systems are presented. The existence of theexact traveling-wave solutions is in general extremely helpful inthe theoretical and numerical study of thesystems.

Keywords

Field Theory Exact Solution Elementary Particle Quantum Field Theory Wave Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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© Plenum Publishing Corporation 1998

Authors and Affiliations

  • Min Chen

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