Study on Boussinesq-Type equation for biomembranes with amplitude and displacement dependent nonlinearity

Purpose We will discuss in detail how the Boussinesq-type wave equation (BWE) represent the physical properties of the biomembrane in an amplitude and displacement dependent manner, particularly the correspondence of various parameters in the equation in biological systems. With this study, we tried to complete the deficiencies we saw in the literature, obtain analytical solutions. Design/methodology/approach In the literature, many analytical methods are used [30–41] whereas in this work, the ansatz-based method with Bernoulli differential equation [57] is considered to obtained analytical solutions of the model. Findings The results can be used for a more detailed analysis of the biomembrane structure and a better explanation of this physical phenomenon. It opens up avenues for physiological experiments on the properties of biomembranes with different structures, such as the application area mentioned in our previous work [57]. Originality/value In this work, wave solutions of BWE for biomembranes are obtained with amplitude-dependent and displacement-dependent nonlinearities, respectively, which to our knowledge is the first time in the literature that this perspective has been considered. It is shown that the behavior of biomembranes depends on the sign of P and Q.