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Discontinuity, Nonlinearity, and Complexity 2(4) (2013) 321--331 | DOI:10.5890/DNC.2013.11.002

Nail H. Ibragimov$^{1}$; Ranis N. Ibragimov$^{2}$

$^{1}$ Laboratory “Group analysis of mathematical models in natural and engineering sciences”, Ufa State Aviation Technical University, 12, K. Marx Str., 450000 Ufa, Russia Research centre ALGA, Department of Mathematics and Science, Blekinge Institute of Technology,

SE-371 79 Karlskrona, Sweden

$^{2}$ Department of Mathematics University of Texas at Brownsville, TX 78520, USA

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Abstract

The concept of dispersion relations is widely used in physics and ap- plied mathematics in investigating wave type solutions of differential equations. On the other hand, Lie group analysis provides another useful method for constructing exact solutions of linear and nonlinear differential equations via the concept of invariant solutions. We show in the present paper that for certain types of differential equations there is a remarkable connection between these two concepts. Namely, the idea of dispersion relations leads to a special type of invariant solutions.

Acknowledgments

NHI acknowledges a financial support of the Government of Russian Federation through Resolution No.220, Agreement No. 11.G34.31.0042.

References

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