Stationary solitons of the fifth order KdV-type. Equations and their stabilization |
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Institution: | 1. School of Mathematics and Statistics, Zhengzhou University, Zhengzhou 450001, China;2. College of Science, Henan University of Technology, Zhengzhou 450001, China;3. College of Mathematics and Information Science, Zhengzhou University of Light Industry, Zhengzhou 450002, China |
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Abstract: | Exact stationary soliton solutions of the fifth order KdV type equation, ut + αupux + βu3x + γu5x = 0, are obtained for any p (> 0) in case αβ > 0, Dβ > 0, βγ < 0 (where D is the soliton velocity), and it is shown that these solutions are unstable with respect to small perturbations in case p ≥ 5. Various properties of these solutions are discussed. In particular, it is shown that for any p these solitons are lower and narrower than the corresponding γ = 0 solitons. Finally, for p = 2 we obtain an exact stationary soliton solution even when D, α, β, γ are all > 0 and discuss its various properties. |
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