The Explicit Solutions Of The Modified B-kind Camassa-holm Equation

It is very important and significance to construct the explicit solutions of themodified b-Kind Camassa-Holm equations. Using the auxiliary differention method, thegeneralized Riccati equation method,(G′/G+G′)‐expansion method and with the aidof the computation system-Maple, many exact solutions of modified b-Kind Camassa-Holm equations have been obtained, which not only include trigonometric eriodic wavesolution, the Jacobi elliptic solutions, exact solitary wave solutions, rational functionsolutions and so on, but also enrich original results. Final, the state and relation of theequation with solution also be analyzed by dynamical system theory.