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

Abstract

Abstract A novel nonlocal   -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.