The existence of generalized solitary wave solutions of a fifth order model equation for steady capillary-gravity waves over a bump with the Bond number near 1/3

摘要

The objective of this paper is to study the existence of generalized solitary wave solutions of a fifth order model equation for steady capillary-gravity waves over a bump with the Bond number near 1/3. We proved that there exist generalized solitary wave solutions of equation, 2F_2η-(3/2)η~2+τ_1η_(xx)-(1/45)η_(xxxx)=b, with τ_1<0 and F_2> 0 for a specific solitary-wave-like non-compact bump (10).