کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
6415207 | 1334972 | 2014 | 45 صفحه PDF | دانلود رایگان |

Considered herein is a modified periodic Camassa-Holm equation with cubic nonlinearity which is called the modified μ-Camassa-Holm equation. The proposed equation is shown to be formally integrable with the Lax pair and bi-Hamiltonian structure. Local well-posedness of the initial-value problem to the modified μ-Camassa-Holm equation in the Besov space is established. Existence of peaked traveling-wave solutions and formation of singularities of solutions for the equation are then investigated. It is shown that the equation admits a single peaked soliton and multi-peakon solutions with a similar character of the μ-Camassa-Holm equation. Singularities of the solutions can occur only in the form of wave-breaking, and several wave-breaking mechanisms for solutions with certain initial profiles are described in detail.
Journal: Journal of Functional Analysis - Volume 266, Issue 2, 15 January 2014, Pages 433-477