ИСТИНА

We consider one-dimensional shallow water equations and look for periodical formal asymptotic solutions in the two case: (a) the basin with two shores, (b) the basin with one shore and vertical wall on the other side. The nonlinear problem is considered in the interval with variable boundary. We consider coordinate transform similar to linearized Carrier–Greenspan transform that “fixes” the boundary. For resulting system periodical formal asymptotics can be constructed. The error of such formal asymptotics appears to be small in the case when nonlinear waves does not break. Constructed asymptotics are compared with experimental results and fit well. Standing waves in experimental vessel are induced by vertical oscillations with parametric resonance. We consider two shapes of bottom (a) parabolic (asymptotics are defined using the Legendre polynomials) and (b) slopping with vertical wall. Considered approach provides effective analytical-numerical algorithm for finding approximate solutions.