  In the present work, the current-voltage (I-V) characteristics in a coupled
long Josephson junction based on magnesium diboride are studied by establishing
a system of equations of phase differences of various inter- and intra-band
channels starting from the microscopic Hamiltonian of the junction system and
simplifying it through the phenomenological procedures such as action,
partition function, Hubbard-Stratonovich transformation (bosonization),
Grassmann integral, saddle-point approximation, Goldstone mode, phase dependent
effective Lagrangian and, finally, Euler-Lagrange equation of motion. The
system of equations are solved using finite difference approximation for which
the solution of unperturbed sine-Gordon equation is taken as the initial
condition. Neumann boundary condition is maintained at both the ends so that
the fluxon is capable of reflecting from the end of the system. The phase
dependent current is calculated for different tunnel voltage and averaged out
over space and time. The current-voltage characteristics are almost linear at
low voltage and non-linear at higher voltage which indicates that the more
complicated physical phenomena at this situation may occur. At some region of
the characteristics, there exist a negative resistance which means that the
junction system can be used in specific electronic devices such as oscillators,
switches, memories etc. The non-linearity is also sensitive to the layer as
well as to the junction thicknesses. Non-linearity occurs for lower voltage and
for higher junction and layer thicknesses.
