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Traveling wave solutions of the BBM-like equations. (English) Zbl 1185.37155

The author applies the factorisation technique for second order ordinary differential equations to find classes of travelling waves for the Benjamin-Bona-Mahony-like equation \(u_t+u_x + a(u^m)_x-(u^n)_{xxt}=0\), where \(m,n>1\), \(m\neq n\). These are expressed in terms of Weierstrass functions.

MSC:

37K40 Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems
35Q53 KdV equations (Korteweg-de Vries equations)
33E05 Elliptic functions and integrals
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