2019/09/02 by Č. Burdík, Burdik, Cestmir, Gaukhar Shaikhova +3
Engineering · Physics and Astronomy · #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #Photonic Crystal and Fiber Optics
paper · pdf · doi:10.48550/arxiv.1909.00826
openalex publication_date 2019/09/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we present the two-dimensional generalized nonlinear\nSchr "odinger equations with the Lax pair. These equations are related to many\nphysical phenomena in the Bose-Einstein condensates, surface waves in deep\nwater and nonlinear optics. The existence of the Lax pair defines integrability\nfor the partial differential equation, so the two-dimensional generalized\nnonlinear Schr "odinger equations are integrable. We obtain bilinear forms of\nthe two-dimensional GNLS equations. One- and two-soliton solutions are derived\nvia the Hirota bilinear method, a procedure quite useful in the solution of\nnonlinear partial differential equations. We apply the extended tanh method in\norder to construct new exact traveling wave solutions. Through 3D plots, we\nshow the dynamical behavior of the obtained solutions.\n