Dali Xu

TL;DR: In this article, the steady-state fully resonant wave system, consisting of two progressive primary waves in finite water depth and all components due to nonlinear interaction, is investigated in detail by means of analytically solving the fully nonlinear wave equations as a nonlinear boundary-value problem.

TL;DR: The steady-state nearly resonant water waves with time-independent spectrum in deep water are obtained from the full wave equations for inviscid, incompressible gravity waves in the absence of surface tension by means of a analytic approximation approach based on the homotopy analysis method (HAM) as mentioned in this paper.

TL;DR: In this paper, the steady-state wave spectra are quantitatively observed within the inherent system error of the basin and identified by means of a contrasting experiment, and the experimental and theoretical results show excellent agreement.

TL;DR: In this paper, a new kind of auxiliary linear operator is proposed to transform the small divisors associated with the non-trivial nearly resonant components to singularities associated with exactly resonant ones.

TL;DR: In this article, the mass, momentum, and energy flux conservation analysis between the linear and nonlinear steady-state wave groups is provided by means of the homotopy analysis method, where the small divisors associated with nearly resonant components are transformed to singularities that are originally caused by exact resonances by a piecewise auxiliary linear operator.