Variational Principles and Solitary Wave Solutions of Generalized ‎Nonlinear Schrödinger Equation in the Ocean

• Published in: Journal of applied and computational mechanics Vol. 7; no. 3; pp. 1639 - 1648
• Main Authors: Meng-Zhu Liu, Xiao-Qun Cao, Xiao-Qian Zhu, Bai-Nian Liu, Ke-Cheng Peng
• Format: Journal Article
• Language: English
• Published: Shahid Chamran University of Ahvaz 01.07.2021
• Subjects: generalized nonlinear schrödinger equation; internal solitary waves; semi-inverse method; variational principle
• ISSN: 2383-4536; 2383-4536
• DOI: 10.22055/jacm.2021.36690.2890

Internal solitary waves are very common physical phenomena in the ocean, which play an important role in the transport of marine matter, momentum and energy. Because the generalized nonlinear Schrödinger equation can well explain the effects of nonlinearity and dispersion in the ocean, it is more suitable for describing the deep-sea internal wave propagation and evolution than other mathematical models. At first, by designing skillfully the trial-Lagrange functional, different kinds of variational principles are successfully established for a generalized nonlinear Schrödinger equation by the semi-inverse method. Then, the constructed variational principles are proved correct by minimizing the functionals with the calculus of variations. Furthermore, some kinds of internal solitary wave solutions are obtained and demonstrated by semi-inverse variational principle for the generalized nonlinear Schrödinger equation.