Breather, Soliton and Rational Solutions for the (2 + 1)-Dimensional Hirota Equation

Abstract

By virtue of Hirota’s bilinear method and Kadomtsev-Petviashvili hierarchy reduction technique, the general breather, soliton and rational solutions in the (2 + 1)-dimensional Hirota equation are constructed. These solutions are expressed in terms of Gram determinants and Schur polynomials. The Nth-order breather and soliton solutions contain 2N free complex parameters, while Nth-order rational ones possess N free complex parameters. By utilizing the Hermitian matrices, the range of free parameters is determined such that it ensures the regularity of these breather and soliton solutions. For the rational solutions, their non-singularity is proved and the parity-time-symmetric condition is derived. Furthermore, the rich dynamic patterns of breather, soliton and rational solutions are established by various choices of free parameters.

Keywords

Hirota’s bilinear method / Kadomtsev-Petviashvili hierarchy reduction technique / (2 + 1)-Dimensional Hirota equation / 37K40 / 35Q53

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