인문학
사회과학
자연과학
공학
의약학
농수해양학
예술체육학
복합학
DBpia AI
AI 에이전트
AI 아이디어
AI 리더
AI 뷰어
Citeasy
크롬 서지관리 다운로드
지원사업
학술연구/단체지원/교육 등 연구자 활동을 지속하도록 DBpia가 지원하고 있어요.
커뮤니티
연구자들이 자신의 연구와 전문성을 널리 알리고, 새로운 협력의 기회를 만들 수 있는 네트워킹 공간이에요.
초록·키워드
This study investigates the Modified Complex Ginzburg-Landau Equation, a fundamental nonlinear partial differential equation that plays a central role in modeling complex wave dynamics, pattern formation, and dissipative phenomena in systems such as nonlinear optics, Bose-Einstein condensates, superfluids, and plasmas. Despite its importance, obtaining exact analytical solutions and understanding their stability properties remain challenging problems with significant theoretical and practical implications. To address this challenge, the Modified Extended Direct Algebraic Method is employed to construct exact analytical solutions in a systematic and efficient manner. By transforming the governing nonlinear equation into an algebraically solvable system, a broad and unified family of exact solutions is derived. These solutions include bright and dark solitons, singular solutions, periodic and singular periodic waves, as well as solutions expressed in exponential, Weierstrass elliptic, and Jacobi elliptic function forms. In addition, a comprehensive stability analysis is carried out to examine the response of these wave structures to small perturbations and to assess their long-term dynamical behavior. The physical characteristics and dynamical features of the obtained solutions are illustrated through detailed two-dimensional and three-dimensional graphical representations for selected parameter values. The results demonstrate the effectiveness of the Modified Extended Direct Algebraic Method in analyzing complex nonlinear models and provide deeper insight into wave propagation and stability mechanisms in dissipative systems governed by the Modified Complex Ginzburg-Landau Equation.
인공지능 문자 인식 모델을 통해 추출된 텍스트로, 일부 오타나 오류가 포함될 수 있으나 지속적으로 개선 중입니다.
오류를 발견하셨다면 해당 부분을 드래그한 후 ' 를 통해 신고해주세요.
오류를 발견하셨다면 해당 부분을 드래그한 후 ' 를 통해 신고해주세요.
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