Soliton perturbation theory for the compound KdV equation. (English) Zbl 1147.35346

Summary: The soliton perturbation theory is used to study the solitons that are governed by the compound Korteweg de-Vries equation
\[ q_t+(aq^p+bq^{2p})q_x+cq_{xxx}=\varepsilon R \] where \(\varepsilon\) is the perturbation parameter and \(0<\varepsilon\ll 1\), in presence of the perturbation terms \(R=\alpha q+\beta q_{xx}+\gamma q^mq_x+\delta q_x^3\) with \(\alpha,\beta\) small dissipative coefficients, \(\gamma\) the coefficient of higher order nonlinear dispersive term, and \(m\) a positive integer \(1\leq m\leq 4\). The adiabatic parameter dynamics of the solitons in presence of the perturbation terms are obtained.


35Q53 KdV equations (Korteweg-de Vries equations)
35Q51 Soliton equations
37K40 Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems


Full Text: DOI


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