This paper employs the principle of undetermined coefficients to establish the hyperbolic and trigonometric function solutions of the coupled sine-Gordon equation (CSGE) which describes the propagation of an optical pulse in fiber waveguide. Lie point symmetry of the CSGE is derived. Previously, it was noticed that the concept of nonlinear self-adjointness (NSA) was not applied on the equation under consideration. Here, we apply the concept of NSA to find an explicit form of the differential substitution. By means of the obtained substitution, we establish a new variant of conserved vectors by a new conservation theorem.

中文翻译：

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非线性光学中耦合正弦-戈登方程的孤子动力学

本文利用待定系数原理建立了耦合正弦-戈登方程（CSGE）的双曲和三角函数解，该方程描述了光脉冲在光纤波导中的传播。推导出 CSGE 的李点对称性。以前，人们注意到非线性自伴随（NSA）的概念并未应用于所考虑的方程。在这里，我们应用 NSA 的概念来找到微分替换的显式形式。通过获得的替换，我们通过新的守恒定理建立了守恒向量的新变体。