Abstract. Nonlinear wave-wave interactions among ocean surface waves are dominated by quadruplet wave-wave interactions. Computing the nonlinear 4-wave interactions with the Boltzmann integral requires finding the loci of interactions for the quadruplets or solving the delta functions. This is an important part of the computation, but so far it is done by an iteration method that consumes computational time and may not converge after doing several iterations. In this paper, an explicit methodology to find the loci of the quadruplet interactions is presented. This research target is to develop a better method to compute the loci. To illustrate the method, there are 4 cases that will be discussed in this paper. Results show that the new method gives better results than the previous methods that have been applied. Moreover, without iterations the presented method requires less computational loops and some variables, for example the distance between loci, denoted ds, can be determined without any looping. Therefore, the new method leads to better and faster computations than the previous iteration method.
A new method to integrate (2+1)-wave equations with Dirac's delta functions as sources