THE CONCAVE OR CONVEX PEAKED AND SMOOTH SOLITON SOLUTIONS OF CAMASSA-HOLM EQUATION

摘要

The traveling wave soliton solutions and pair soliton solution to a class of new completely integrable shallow water equation, Camassa_Holm equation are studied. The concept of concave or convex peaked soliton and smooth soliton were introduced. And the research shows that the traveling wave solution of that equation possesses concave and convex peaked soliton and smooth soliton solutions with the peakson. Simultaneously by applying Backlund transformation the new pair soliton solutions to this class of equation are given.