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Stability of multi-compacton solutions and Bäcklund transformation in $K(m,n,1)$. (English) Zbl 1075.37028
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.

37K35Lie-Bäcklund and other transformations
35Q53KdV-like (Korteweg-de Vries) equations
35B35Stability of solutions of PDE
35A30Geometric theory for PDE, characteristics, transformations
37K40Soliton theory, asymptotic behavior of solutions
Full Text: DOI
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