Head-on collision of solitary waves in coupled Korteweg–de Vries systems modeling nonlinear transmission lines

• Head-on collision of solitons in coupled Korteweg–de Vries systems is characterized.
• The extended Poincaré–Lighthill–Kuo method is applied.
• Collision-induced phase shifts are evaluated for each propagation mode.
• The governing wave equation for collision-induced pulses is derived.

The extended Poincaré–Lighthill–Kuo (PLK) method is applied to characterize head-on collisions of solitary waves in a coupled Korteweg–de Vries (KdV) system that has multiple modes supporting solitons. As a simple physically realizable system, we investigate two coupled electrical nonlinear transmission lines (NLTLs), and the proposed method successfully leads to the collision-induced phase shifts and the wave equation that governs the dynamics of the pulses generated by colliding solitary waves.