Abstract
In the present paper, with the aid of symbolic computation, families of new nontrivial solutions of first-order elliptic equation ϕ′ 2 = a 0 + a 1 ϕ + a 2 ϕ 2 + a 3 ϕ 3 + a 4 ϕ 4 (where ϕ ′ = d d x ϕ ) are obtained. To our knowledge, these nontrivial solutions can not be found in [Chaos Solitons Fract. 26 (2005) 785–794] and [Phys. Lett. A 336 (2005) 463–476] by Yomba and other existent papers until now. By using these nontrivial solutions, a direct algebraic method is described to construct several kinds of exact non-travelling wave solutions for the (2 + 1)-dimensional Breaking soliton equations and the (2 + 1)-dimensional asymmetric Nizhnik–Novikov–Vesselov equation. By using this method, many other physically important nonlinear partial differential equations (NLPDEs) can be investigated and new non-travelling wave solutions can be explicitly obtained with the aid of symbolic computation system Maple.
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