We study soliton solutions to the DKP equation which is defined by the Hirotabilinear form, \[ {\begin{array}{llll} (-4D_xD_t+D_x^4+3D_y^2)\tau_n\cdot\tau_n=24\tau_{n-1}\tau_{n+1}, (2D_t+D_x^3\mp 3D_xD_y) \tau_{n\pm1}\cdot\tau_n=0 \end{array} \quad n=1,2,.... \] where $\tau_0=1$. The$\tau$-functions $\tau_n$ are given by the pfaffians of certain skew-symmetricmatrix. We identify one-soliton solution as an element of the Weyl group ofD-type, and discuss a general structure of the interaction patterns among thesolitons. Soliton solutions are characterized by $4N\times 4N$ skew-symmetricconstant matrix which we call the $B$-matrices. We then find that one can have$M$-soliton solutions with $M$ being any number from $N$ to $2N-1$ for some ofthe $4N\times 4N$ $B$-matrices having only $2N$ nonzero entries in the uppertriangular part (the number of solitons obtained from those $B$-matrices waspreviously expected to be just $N$).
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机译：我们研究由Hirotabilinear线性形式\ [{\ begin {array} {llll}（-4D_xD_t + D_x ^ 4 + 3D_y ^ 2）\ tau_n \ cdot \ tau_n = 24 \ tau_ {定义的DKP方程的孤子解。 n-1} \ tau_ {n + 1}，（2D_t + D_x ^ 3 \ mp 3D_xD_y）\ tau_ {n \ pm1} \ cdot \ tau_n = 0 \ end {array} \ quad n = 1,2，.. .. \]其中$ \ tau_0 = 1 $。 $ \ tau $函数$ \ tau_n $由某些斜对称矩阵的pfaffians给出。我们将单孤子解决方案确定为D型Weyl基团的一个元素，并讨论了孤子之间相互作用模式的一般结构。孤子解的特征是$ 4N×4N $偏对称常数矩阵，我们称其为$ B $矩阵。然后我们发现一个可以有$ M $孤子解，其中$ M $是从$ N $到$ 2N-1 $的任意数字，对于某些$ 4N \乘以4N $ $ B $矩阵，其中只有$ 2N $非零上三角部分中的项（从这些$ B $矩阵获得的孤子数以前预计仅为$ N $）。
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