It is well-known that the celebrated Camassa-Holm equation has the peaked solitary waves,which have been not reported for other mainstream models of shallow water waves.In this letter,the closed-form solutions of peak...It is well-known that the celebrated Camassa-Holm equation has the peaked solitary waves,which have been not reported for other mainstream models of shallow water waves.In this letter,the closed-form solutions of peaked solitary waves of the KdV equation,the BBM equation and the Boussinesq equation are given for the first time.All of them have either a peakon or an anti-peakon.Each of them exactly satisfies the corresponding Rankine-Hogoniot jump condition and could be understood as weak solution.Therefore,the peaked solitary waves might be common for most of shallow water wave models,no matter whether or not they are integrable and/or admit breaking-wave solutions.展开更多
基金supported by the State Key Lab of Ocean Engineering(Grant No.GKZD010056-6)the National Natural Science Foundation of China(Grant Nos.10872129 and 11272209
文摘It is well-known that the celebrated Camassa-Holm equation has the peaked solitary waves,which have been not reported for other mainstream models of shallow water waves.In this letter,the closed-form solutions of peaked solitary waves of the KdV equation,the BBM equation and the Boussinesq equation are given for the first time.All of them have either a peakon or an anti-peakon.Each of them exactly satisfies the corresponding Rankine-Hogoniot jump condition and could be understood as weak solution.Therefore,the peaked solitary waves might be common for most of shallow water wave models,no matter whether or not they are integrable and/or admit breaking-wave solutions.
