Qualitative analysis and exact solutions to the Burgers-Korteweg-de Vries equation. (English) Zbl 1017.35100
Summary: Using the qualitative theory of ordinary differential equations, we give a qualitative analysis to a two-dimensional plane autonomous system which is equivalent to the Burgers-Korteweg-de Vries equation. Then applying the theory of commutative algebra and the first-integral method, we obtain exact solutions to the Burgers-Korteweg-de Vries equation. The results indicate that the solutions obtained in the literature are the particular cases of our results.
MSC:
35Q53 | KdV equations (Korteweg-de Vries equations) |
37K20 | Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with algebraic geometry, complex analysis, and special functions |
35C05 | Solutions to PDEs in closed form |