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Examines stability of KdV solitons on the half-line, suggesting important implications for nonlinear dynamics.
We study the orbital stability and asymptotic stability problems for KdV solitons on the right half‐line for nonhomogeneous boundary conditions in the energy space . This paper improves the results of Cavalcante and Muñoz [ Revista Matemática Iberoamericana 35, no. 6 (2019); and SIAM Journal on Mathematical Analysis 55, no. 5 (2023): 4193–5992], which treat the homogeneous case. One of the key components of the stability argument in this work is the refinement of the estimate for the Lyapunov functional, given that the mass and energy, unlike in the context of homogeneous boundary conditions, do not exhibit a dissipative mechanism. As a consequence of this analysis, we obtain global control of the trace of the first and second derivatives of the solution to the model. This is, as far as we understand, the first orbital and asymptotic stability result for solitons posed on a half‐line in the context of nonhomogeneous boundary conditions.
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Campos et al. (2026) studied this question.
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