Benjamin-Ono equation: Rogue waves, generalized breathers, soliton bending, fission, and fusion

Singh, Sudhir; Sakkaravarthi, K.; Murugesan, K.; Sakthivel, R.

doi:10.1140/epjp/s13360-020-00808-8

Cited by 20 publications

(1 citation statement)

References 38 publications

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“…To date, some methods have been proposed and applied to investigate localized waves of coupled systems, such as the Darboux transformation (DT) [18], the Riemann-Hilbert approach [19], the Hirota bilinear method [20], the generalized DT [21], and so on. Due to the profound theoretical significance and potential applicability, the study of localized waves of the nonlinear PDEs has always been concerned, and great progress has been made [22][23][24][25][26][27][28][29].…”

Section: Introductionmentioning

confidence: 99%

Localized Waves for the Coupled Mixed Derivative Nonlinear Schrödinger Equation in a Birefringent Optical Fiber

Song

Lei

Zhang

et al. 2022

J Nonlinear Math Phys

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In this paper, the higher-order localized waves for the coupled mixed derivative nonlinear Schrödinger equation are investigated using generalized Darboux transformation. On the basis of seed solutions and a Lax pair, the first- and second-order localized wave solutions are derived from the Nth-order iteration formulas of generalized Darboux transformation. Then, the dynamics of the localized waves are analyzed and displayed via numerical simulation. It is found that the second-order rouge wave split into three first-order rogue waves due to the influence of the separation function. In addition, a series of novel dynamic evolution plots exhibit that rogue waves coexist with dark-bright solitons and breathers.

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