| Abstract: |
| Considered here is a system
$$\partial_t u+\partial_xu-\partial_{xxt}u +\partial_x\partial_u H(u, v)=0, $$
$$\partial_t u+\partial_xu-\partial_{xxt}u +\partial_x \partial_v H(u, v)=0$$
of nonlinear dispersive equations, where $u=u(x,t), v=v(x, t)$ are real-valued functions, and $H$ is a homogeneous polynomial function of degree $p\geq 3.$
We present existence of explicit solitary wave solutions. A simple algebraic condition for stability of the explicit solitary wave solution is derived. Criteria for instability of explicit solitary wave solutions are obtained as well. |
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