Abstract
The Broer-Kaup system with corrections is considered. Based on the inverse scattering transform, we extend the perturbation theory to discuss the adiabatic approximate solution and ε-order approximate solution of one soliton to the Broer-Kaup system with corrections.
Highlights
The coupled integrable system or the Broer-Kaup (BK) system [1–5] tt = Àv2 + − Á vx, x ð1Þ ωt = vω1 2 ωx ð2Þ is related to one of the Boussinesq systems by variable transformation
Kaup first proposed the perturbation theory based upon the inverse scattering transform [6]
In addition to the perturbation theory based upon the inverse scattering transform [7–15], there are many other methods, such as the direct soliton perturbation theory [16–30] and the normal form method [31–34]
Summary
1 2 ωx ð2Þ is related to one of the Boussinesq systems by variable transformation. The BK system is used to simulate the bidirectional propagation of long waves in shallow water. Kaup first proposed the perturbation theory based upon the inverse scattering transform [6]. We consider the BK system with corrections through perturbation theory based upon the inverse scattering transform [15] and investigate the adiabatic approximate solution and ε-order approximate solution of one soliton to the BK system with corrections. In order to carry out the inverse scattering transform to discuss the BK system with corrections, we keep the first Lax equation but give up the second one. For this reason, the analyticity and asymptotic behaviors of Jost functions are the same as the BK system.
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