摘要
We investigate the KdV like equation with higher order nonlinearity ut + a(1 +bun)unux + uxxx = 0with n ≥ 1, a, b ∈ R and α≠ 0. The bifurcations and explicit expressions of solitary wave solutions for theequation are discussed by using the bifurcation method and qualitative theory of dynamical systems. Thebifurcation diagrams, existence and number of the solitary waves are given.
We investigate the KdV like equation with higher order nonlinearity $$u_t + a\left( {1 + bu^n } \right)u^n u_x + u_{xxx} = 0$$ withn ? 1,a, b ∈R anda ≠ 0. The bifurcations and explicit expressions of solitary wave solutions for the equation are discussed by using the bifurcation method and qualitative theory of dynamical systems. The bifurcation diagrams, existence and number of the solitary waves are given.
基金
This work was supported by the National Natural Science Foundation and the National Key Basic Research Special Fund (Grant No.G1998020307) of China.
