Numerical calculation and characteristics of quasi-periodic breathers to the Kadomtsev–Petviashvili-based system

Abstract

The Kadomtsev–Petviashvili-based system can be regarded as a consistent approximation of a class of partial differential equations, which can be used to describe the nonlinear wave phenomena in the fields of ionomers, fluid dynamics and optical systems. In this paper, an effective method is introduced to study the quasi-periodic breathers of the Kadomtsev–Petviashvili-based system. Based on the Hirota’s bilinear method and the Riemann-theta function, an over-determined system about quasi-periodic breathers can be obtained. It can be integrated into a least square problem and solved by the numerical iterative algorithms. The asymptotic properties of the quasi-periodic 1-breathers are analyzed rigorously under the small amplitude limit. The dynamic behaviors including the periodicity and distance between two breather chains of the quasi-periodic breathers are analyzed precisely by an analytic method related to the characteristic lines. The effective method presented in this paper can be further extended to the other integrable systems with breathers.