N-soliton solutions and the Hirota conditions in (2+1)-dimensions

• Published in: Optical and quantum electronics Vol. 52; no. 12
• Main Author: Ma, Wen-Xiu
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.12.2020; Springer Nature B.V
• Subjects: Algorithms; Characterization and Evaluation of Materials; Computer Communication Networks; Electrical Engineering; Homogeneity; Lasers; Mandarins; Optical Devices; Optics; Photonics; Physics; Physics and Astronomy; Polynomials; Solitary waves; Soliton solution; Hirota; Secondary; (2+1)-Dimensional integrable equations; 35Q53; 37K40; 35Q51; soliton condition
• ISSN: 0306-8919; 1572-817X
• DOI: 10.1007/s11082-020-02628-7

We compute N -soliton solutions and analyze the Hirota N -soliton conditions, in (2+1)-dimensions, based on the Hirota bilinear formulation. An algorithm to check the Hirota conditions is proposed by comparing degrees of the polynomials generated from the Hirota function in N wave vectors. A weight number is introduced while transforming the Hirota function to achieve homogeneity of the resulting polynomial. Applications to three integrable equations: the (2+1)-dimensional KdV equation, the Kadomtsev–Petviashvili equation, the (2+1)-dimensional Hirota–Satsuma–Ito equation, are made, thereby providing proofs of the existence of N -soliton solutions in the three model equations.