Abstract
We propose the new discrete modified KdV equation defined as u i =4(u i-1 -u i+1 )/[(1-u i-1 -u i ) 1/2 (1+u i +u i+1 ) 1/2 +(1+u i +u i ) 1/2 (1-u i -u i= i1) 1/2 ] 2 . We discuss the transformation relations among the new discrete modified KdV equation, the discrete modified KdV equation, the discrete KdV equation, and the Volterra equation. We transform the new discrete modified KdV equation to seven bilinear forms, and prove its N-soliton solution. We also find a 1-soliton solution under a nonvanishing boundary condition by taking a limit of the modulus in the already-known elliptic function solution
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