Abstract
Based on the Hirota bilinear method and theta function identities, we obtain a new type of doubly periodic standing wave solutions for a coupled Higgs field equation. The Jacobi elliptic function expression and long wave limits of the periodic solutions are also presented. By selecting appropriate parameter values, we analyze the interaction properties of periodic-periodic waves and periodic-solitary waves by some figures.
Highlights
As is well known, the investigation of the explicit exact solutions to nonlinear evolution equations (NLEEs) plays an important role in the study of nonlinear physical phenomena [1, 2]
The combination of the Hirota bilinear method and theta function identities is demonstrated to be a powerful tool in finding periodic waves for the coupled Higgs field equation
We have derived a new kind of doubly periodic standing wave solutions for the coupled Higgs field equation, which is different from those of the known solutions reported in the literature
Summary
The investigation of the explicit exact solutions to nonlinear evolution equations (NLEEs) plays an important role in the study of nonlinear physical phenomena [1, 2]. We will focus on a coupled Higgs field equation with important physical interests [19], utt − uxx − βu + δ|u|2u − 2uV = 0, (1). The Hirota bilinear method is a powerful tool for constructing various exact solutions for NLEEs, which include soliton, negaton, rogue waves, rational solutions, and quasiperiodic solutions [25–35]. The focus of this work is to investigate new types of doubly periodic standing wave solutions for (1).
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