Abstract
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.
•A new integrable PDE model of sixth-order.•An innovative algorithm to verify the Hirota N-soliton condition.•Existence of N-solion solutions under general dispersion relations.