We consider a linear combination of the potential KP equation and the BKP equation, and call it a combined pKP–BKP equation. We prove that the combined pKP–BKP equation satisfies the Hirota $N$-soliton condition and thus it possesses an $N$-soliton solution. The proof is an application of an algorithm to compare degrees of homogeneous polynomials associated with the Hirota function in $N$ wave vectors.

中文翻译：

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$ñ$pKP–BKP方程的孤子解

我们考虑了潜在的KP方程和BKP方程的线性组合，并将其称为pKP–BKP组合方程。我们证明组合的pKP–BKP方程满足Hirota$ñ$-孤子条件，因此它具有一个 $ñ$-孤子解决方案。该证明是一种算法的应用，用于比较与Hirota函数相关的齐次多项式的阶数$ñ$ 波向量。