Shallow Water Wave Models with and without Singular Kernel: Existence, Uniqueness, and Similarities

Figure 1

Representation of the solution when in (a) and (b) and in (c) and (d) with both Caputo derivative and Caputo-Fabrizio derivative. As expected, similar behaviors are pointed out in each case and we can see the existence of multisoliton solutions for both types of equations.

(a) Caputo representation

(b) Caputo-Fabrizio representation

(c) Caputo representation

(d) Caputo-Fabrizio representation