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New solutions of several kinds of auxiliary equations, Bcklund transformation and nonlinear superposition formula of the solutions are presented by studying a highly auxiliary equation method. Based on this and different m and n, the method of combining transformation and direct integration is used to obtain infinite sequence new exact solutions of K(m,n) equation and B(m,n) equation, which include infinite sequence smooth soliton solutions, peak soliton solutions and compact soliton solutions.
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Keywords:
- auxiliary equation method/
- direct integration/
- K(m,n) equation and B(m,n) equation/
- infinite sequence exact solution
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