Abstract
The method combining the auxiliary equation, the function transformation and the variable separation solutions was proposed to construct the new 2-soliton and 2-period solutions to the arbitrary order nonlinear Camassa-Holm equation. Step 1, with 2 auxiliary equations, the function transformation and the variable separation solutions, the problem of solving the arbitrary order nonlinear Camassa-Holm equation was transformed to the problem of solving the nonlinear algebraic equations. Step 2, by means of symbolic computation system Mathematica, the solutions to the algebraic equations were obtained, and with the help of the relative conclusions on the auxiliary equation, the new 2-soliton and 2-period solutions were constructed.
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