【摘要】 Sinh-Gordon方程是典型的可积系统，精确孤子解和周期解是证明其可积性的关键证据。为了用非线性解建立可积系统的范式，研究以变量分离法和初等积分法为基础，把求解Sine-Gordon方程的基本方法拓展性地应用于求解Sinh-Gordon方程，得到了数量众多新的非线状周期解、孤子解和极为罕见的呼吸孤子解，更好地刻画了晶体错位、自旋链激发、超导约瑟夫森结中的非线性现象。更多还原

【Abstract】 The sinh-Gordon equation is a typical integrable system, whose exact soliton and periodic solutions constitute crucial evidence for verifying its integrability. Based on the separable variable method and elementary integral method, the solutions to Sinh-Gordon equation were studied by extending the original method used for solving SineGordon equation. A number of nonlinear periodic solutions, soliton solutions, and rare respiratory soliton solutions were obtained. These nonlinear solutions not only help establish the theoretical paradigm for integrable systems but also provide an effective tool to characterize nonlinear phenomena in crystal dislocation, spin chain excitation, and superconducting Josephson junctions.更多还原