The coupled Higgs field equation is significant for describing a system of conserved scalar nucleons interacting with the neutral scalar meson. The improved Bernoulli sub-equation function method and the sine–Gordon expansion method have been put in used in the current article, to interpret the dynamism of the particles through analytical solutions modelled by the coupled Higgs field equation. The interaction among the electrons and mesons has been found out and it is observed that the particle moves along the smooth path from one state to another. It is also vital to mark that the wave profile of the waves are velocity dependent and the incident is shown in the figures. Different types of soliton shape like, bell shape soliton, kink soliton, consolidated bell shape; anti-bell shape soliton, compacton, singular soliton, flat kink soliton etc. are ascertained by assigning individual quantities of the unidentified parameters whose propagations are portrayed in 3D and 2D surfaces. The solutions established in this study are further comprehensive, broad–ranging and some are new which have not been found in earlier research. The executed schemes are effective, compatible to computer algebra and deliver ample wide–ranging wave solutions.

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通过解析解寻找耦合希格斯场方程描述的现象的相互作用

耦合希格斯场方程对于描述与中性标量介子相互作用的守恒标量核子系统很重要。本文使用了改进的伯努利子方程函数方法和正弦-戈登展开方法，通过耦合希格斯场方程建模的解析解来解释粒子的动力学。已经发现了电子和介子之间的相互作用，并观察到粒子沿着光滑的路径从一种状态移动到另一种状态。同样重要的是要标记波浪的波形与速度有关，并且图中显示了事件。不同类型的孤子形状，如钟形孤子、扭结孤子、合并钟形；反钟形孤子、压实孤子、奇异孤子、平扭孤子等。通过分配未识别参数的单个数量来确定其传播在 3D 和 2D 表面中描绘。本研究中建立的解决方案更加全面、广泛，有些是早期研究中未发现的新解决方案。执行的方案是有效的，与计算机代数兼容，并提供丰富的宽范围波解决方案。