The tanh and the sine-cosine methods for a reliable treatment of the modified equal width equation and its variants.

*(English)*Zbl 1078.35108Summary: The modified equal width equation

$${u}_{t}+3{u}^{2}{u}_{x}-\alpha {u}_{xxt}=0$$

and two of its variants are investigated. The strategy here rests mainly on a sine-cosine ansatz and the tanh method. Both schemes work well and reveal exact solutions with distinct physical structures. The obtained solutions include compactons, solitons, solitary patterns, and periodic solutions.

##### MSC:

35Q53 | KdV-like (Korteweg-de Vries) equations |

37K40 | Soliton theory, asymptotic behavior of solutions |

35C05 | Solutions of PDE in closed form |

65M99 | Numerical methods for IVP of PDE |