Modulational Instability and Location Controllable Lump Solutions with Mixed Interaction Phenomena for the (2+1)-Dimensional Myrzakulov-Lakshmanan-IV Equation

Abstract Under consideration is a $$(2+1)$$ ( 2 + 1 ) -dimensional spin nonisospectral Myrzakulov-Lakshmanan-IV (ML-IV) equation, which has close relation with the celebrated nonlinear Schrödinger equation. In first place we study modulational instability (MI) for this equation and deduce its formation mechanism diverse localized waves from plane wave background. Secondly, in view of known Lax pair successfully extend generalized $$(n, N-n)$$ n , N - -fold Darboux Transformation (DT) $$(1+1)$$ to As an application resulting DT, derive some location controllable dark bright lump, periodic mixed breather-lump solutions, it shown that position these can be controlled by special parameters, so move them positions want. Especially, dynamical behaviors are illustrated graphically. These results may have potential value applied ferromagnetism nano magnetism.