Capacitive NLTL Solitary Wave Equation with Mutual Inductance

We have studied and developed the solitary wave solution in dissipative capacitive non-linear transmission lines that are described by $u_{\tau}+6uu_{x}+u_{xxxx}=0$ , which includes nonlinear term similar to the KdV equation with the corresponding fifth-order dispersion term. We have accounted for the mutual inductance effect from the corresponding neighboring inductors in contrast to the previously reported conventional capacitive NLTL solutions. The proposed equation has been verified by experiments and it has been shown that it holds valid in both weak and strong capacitive non-linearity scenarios.