Oblique Interaction of Solitary Waves

Numerical study of the KP equation for non-periodic waves

“…From the chord diagram in Figure 3.3, one can see that the asymptotic line-solitons are given by [1,3]-and [2, 4]types for both y → ±∞. The solution in this case corresponds to the top cell of Gr (2,4), and the A-matrix is given by…”

“…gives the x-intercept of the line of the [i, j]-soliton for x 0 at t = 0), and r for the on-set of the box. The phase shifts for [1,3]-and [2,4]-solitons are given by ∆x [i, j]…”

“…In Figure 3.4, we have chosen those parameters as s = 1, Θ + [1,3] = Θ + [2,4] = 0 and r = 1, so that at t = 0 the solution forms an X-shape without phase shifts and opening of a box at the origin. In Figure 3.4, the amplitudes are A [1,3] interesting one.…”

“…10 3.3.2. The case π = (4312) From the chord diagram in Figure 3.3, one can see that the asymptotic line-solitons are given by [1,4]-and [2, 3]solitons for y 0 and [1,3]-and [2,4]-solitons in y 0. The A-matrix in this case is given by…”

“…Figure 3.5 illustrates an example of this solution. The parameters in the A-matrix determine the locations of the line-solitons in the following form, 1,3] and c = |3, 1| |4, 3| e Θ + [1,4] .…”