The numerical simulation of colliding solitary waves with compact support arising from the Rosenau-Hyman K(n,n) equation requires the addition of artificial dissipation for stability. The price to pay is the appearance of trailing tails, amplitude damping, and delays as the solution evolves. These undesirable effects can be corrected by properly counterbalancing two sources of artificial dissip...

In this study, a novel method called the q-homotopy analysis transform (q-HATM) is proposed for solving fractional-order Kolmogorov and Rosenau–Hyman models numerically. The shown to have fast convergence demonstrated using test examples. validity of confirmed through graphical representation obtained results, which also highlights ability modify solution’s zone. q-HATM an efficient scheme nonl...

The q-homotopy analysis transform method (q-HATM) is a powerful tool for solving differential equations. In this study, we apply the q-HATM to compute numerical solution of fractional-order Kolmogorov and Rosenau–Hyman models. Fractional-order models are widely used in physics, engineering, other fields. However, their solutions difficult obtain due non-linearity non-locality overcomes these ch...

The numerical simulation of compactons, solitary waves with compact support, is characterized by the presence of spurious phenomena, as numerically-induced radiation, which is illustrated here using four numerical methods applied to the RosenauHyman K(p, p) equation. Both forward and backward radiations are emitted from the compacton presenting a self-similar shape which has been illustrated gr...

Travelling wave solutions are important in nonlinear science. These solutions describe phenomena such as vibrations, solitons and propagation with finite speed. In recent years, direct search for exact solutions of nonlinear partial differential equations (PDEs) has become more and more attractive, partly due to the availability of computer systems like Maple or Mathematica, which allow to perf...

The addition of lysozyme to the survival medium has been shown (Metzger, Hardy, and Nell, 1961) to increase the rate of immobilization of Treponema pallidum by syphilitic serum and complement; this might allow T. pallidum immobilization (TPI) tests to be completed in a working day. But, more important from the point of view of diagnosis, was the possibility of increasing the sensitivity of the ...