## The tanh and the sine-cosine methods for a reliable treatment of the modified equal width equation and its variants.(English)Zbl 1078.35108

Summary: The modified equal width equation $u_t+ 3u^2u_x- \alpha u_{xxt}=0$ 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 equations (Korteweg-de Vries equations) 37K40 Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems 35C05 Solutions to PDEs in closed form 65M99 Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems

ATFM; MACSYMA
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### References:

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