2016/10/22 by Qi-Lao Zha, Zha, QiLao
Mathematics · Physics and Astronomy · #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #Numerical methods for differential equations
paper · pdf · doi:10.48550/arxiv.1610.07051
openalex publication_date 2016/10/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Explicit multi-soliton and multi-peakon solutions of the Dullin-Gottwald-Holm equation are constructed via Darboux transformation and direct computation, respectively. To this end we first map the Dullin-Gottwald-Holm equation to a negative order KdV equation by a reciprocal transformation. Then we use the Darboux matrix approach to derive multi-soliton solutions of the Dullin-Gottwald-Holm equation from the solutions of the negative order KdV equation. Finally, we find multi-peakon solutions of the Dullin-Gottwald-Holm equation in weak sense. For α=(1)/(2) and α≠ (1)/(2), several types of two-peakon solutions are discussed in detail. Moreover, the dynamic behaviors of the obtained solutions are illustrated through some figures.