This study introduces new analytical solutions for the one-line model of shoreline change on bounded coast whose both ends are fixed by the coastal structures or rocky cliffs (solid boundaries). A general analytical solution describing shoreline evolution on the bounded coast with the arbitrary initial shape of beach fill/cut is introduced. Subsequently, several shaped types of initial shorelines, such as trapezoid rectangle, and triangle are considered. The new solutions for the bounded coast (finite coast) were compared with the underlying analytical solutions, which describe shoreline evolution on an infinite coast. This shows the distinct differences in the cases without and with solid boundaries. The solid boundaries lead the shoreline to the equilibrium stage more quickly at a certain position instead of slow and 0 of the case without solid boundaries. The relationship showing the decaying process of sediment in the beach fill portion is presented. Results also highlight that when the value of L*, the ratio of bounded coast length to the width of beach fill portion, is large enough, the shoreline evolution of the cases without solid boundaries is asymptotic even at a large t*. Furthermore, the relationship between the dimensionless decay time, t*, and the dimensionless total length of the adjacent coasts to the beach fill portion is also provided, L_S*, If L_S* is large, then the t* is large and vice versa. The solutions proposed in this study have not been verified with the measured data, which could be a disadvantage. However, the derived solutions could be very useful and beneficial for preliminary design, education practices, and beach nourishment (beach fill), or the recovery of coastal morphology after the severe damages induced by natural disasters (beach cut).

本研究为两端由海岸结构或岩石峭壁（固体边界）固定的有界海岸上的海岸线变化的单线模型引入了新的解析解。介绍了描述具有任意初始海滩填充/切割形状的有界海岸上的海岸线演变的一般解析解。随后，考虑了几种形状类型的初始海岸线，如梯形矩形和三角形。将有界海岸（有限海岸）的新解与描述无限海岸上海岸线演变的基本解析解进行了比较。这显示了没有和有实体边界的情况的明显差异。实心边界使海岸线在某个位置更快地进入平衡阶段，而不是在没有实心边界的情况下缓慢和 0。给出了海滩填埋部分沉积物腐烂过程的关系。结果还突出显示，当L *，有界海岸长度与海滩填充部分宽度的比值足够大，即使在大t * 时，没有实体边界的情况的海岸线演化也是渐近的。此外，还提供了无量纲衰减时间t * 与相邻海岸到海滩填充部分的无量纲总长度L _S * 之间的关系，如果L _S * 很大，则t* 大，反之亦然。本研究中提出的解决方案尚未通过测量数据进行验证，这可能是一个缺点。然而，派生的解决方案对于初步设计、教育实践和海滩营养（海滩填充）或自然灾害引起的严重破坏（海滩切割）后海岸形态的恢复可能非常有用和有益。