Abstract
In this paper, we study the orbital stability of solitary waves of compound KdV-type equation in the form of \({u_t} + a{u^p}ux + b{u^{2p}}ux + {u_{xxx}} = 0\left( {b \geqslant 0,p{\text{ > }}0} \right)\). Our results imply that orbital stability of solitary waves is affected not only by the highest-order nonlinear term \(b{u^{2p}}ux\), but also the nonlinear term \(a{u^p}ux\). For the case of b > 0 and 0 < p ≤ 2, we obtain that the positive solitary wave u1(x−ct) is stable when a > 0, while that unstable when a < 0. The stability for negative solitary wave u 2(x − ct) is on the contrary. In particular, we point that the nonlinear term with coefficient a makes contributes to the stability of the solitary waves when p = 2 and a > 0.
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Supported by the National Natural Science Foundation of China (No.11471215), Innovation Program of Shanghai Municipal Education Commission (No.13ZZ118), Shanghai Leading Academic Discipline Project (No.XTKX2012), and Hujiang Foundation of China (No.B14005).
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Zhang, Wg., Li, Hw., Bu, Xs. et al. Orbital stability of solitary waves of compound KdV-type equation. Acta Math. Appl. Sin. Engl. Ser. 31, 1033–1042 (2015). https://doi.org/10.1007/s10255-015-0525-x
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DOI: https://doi.org/10.1007/s10255-015-0525-x