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Zbl 1075.37028
Tian, Lixin; Yin, Jiuli
Stability of multi-compacton solutions and Bäcklund transformation in $K(m,n,1)$. (English)
[J] Chaos Solitons Fractals 23, No. 1, 159-169 (2005). ISSN 0960-0779

Summary: We introduce a fifth-order $K(m,n,1)$ equation with nonlinear dispersion to obtain multi-compacton solutions by the Adomian decomposition method. Using the homogeneous balance method, we derive a Bäcklund transformation of a special equation $K(2,2,1)$ to determine some solitary solutions of the equation. To study the stability of multi-compacton solutions in $K(m,n,1)$ and to obtain some conservation laws, we present a similar fifth-order equation derived from Lagrangian. We finally show the linear stability of all obtained multi-compacton solutions.

MSC 2000:: *37K35 Lie-Bäcklund and other transformations
35Q53 KdV-like equations
35B35 Stability of solutions of PDE
35A30 Geometric theory for PDE, transformations
37K40 Soliton theory, asymptotic behavior of solutions

Keywords: Adomian decomposition method; solitary solutions

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