Linear superposition for a novel nonlocal PT -symmetric mKdV-sG system

A novel nonlocal PI -symmetric modified Korteweg-de Vries-sine Gordon (mKdV-sG) system is established via the consistent correlated bang (CCB) method from the normal mKdV-sG equation. The obtained nonlocal mKdV-sG system is Lax integrable and can be reduced to the normal mKdV-sG equation with suitable function selections. Using symmetry-antisymmetry separation method, a linear superposition solution theorem for the nonlocal mKdV-sG system is concluded. Abundant nonlinear wave structures of the obtained nonlocal system, such as the periodic waves, the kinks, the breathers and periodic-periodic interaction waves, periodic-kink interaction waves, periodic-breathers interaction waves solutions are obtained from the linear superposition solution theorem.

Automated summary

A novel nonlocal mKdV-sG system is established using the consistent correlated bang method, and abundant nonlinear wave structures are obtained through the linear superposition solution theorem.