The nonlocal nonlinear Schrödinger and Maxwell – Bloch equation

Abstract

In this paper, the nonlocal nonlinear Schrцdinger and Maxwell – Bloch equations are is introduced. A particular case of this system, namely the Schrцdinger equation, is integrable by the inverse scattering method as shown in the work of M. Ablowitz and Z. Musslimani. Following their idea, we prove the integrability of the nonlocal nonlinear Schrцdinger and Maxwell – Bloch equation using its Lax pairs. Also the Darboux transformations are constructed, and soliton solutions are obtained from different "seed" solutions using them. One–fold, two–fold and N–fold determinant representations are obtained by this transformation. Moreover, soliton and solitons–like solutions, such as dynamic and topological soliton, periodic, domain walls, kink, lamp, bright and dark solitons, bright and dark rogue waves, bright and dark positons, etc., of this equation are built. In future papers, we will investigate the conservation laws of the nonlocal nonlinear Schrцdinger and Maxwell – Bloch equation using the Lax pair.

      G M T   Английский Испанский Итальянский Казахский Китайский Трад Китайский Упр Корейский Русский Турецкий Французский   Английский Испанский Итальянский Казахский Китайский Трад Китайский Упр Корейский Русский Турецкий Французский                 Звуковая функция ограничена 200 символами     Настройки : История : Обратная связь : Donate Закрыть