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

Tian, Lixin; Yin, Jiuli

Chaos Solitons Fractals 23, No. 1, 159-169 (2005).

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:

37K35	Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems
35Q53	KdV equations (Korteweg-de Vries equations)
35B35	Stability in context of PDEs
35A30	Geometric theory, characteristics, transformations in context of PDEs
37K40	Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems

Keywords:

Adomian decomposition method; solitary solutions

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