Abstract
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.
Highlights
As is well known, most nonlinear partial differential equations (PDEs) in mathematics and physics are integrable, including the Hirota equation [1], the nonlinear Schrödinger equation [2, 3], the Gerdjikov-Ivanov equation [4], the Korteweg-de Vries equation [5, 6], the Sasa-Satsuma equation [7], and so on
Journal of Nonlinear Mathematical Physics (2022) 29:318–330 researchers than the single-component system [8, 9]. These nonlinear equations can be used to describe and study localized waves, which consist of rogue waves [10, 11], solitons [12, 13], and breathers [14–17]
According to Eqs. (3)–(6), the first- and the second-order localized wave solutions of Eq (1) are obtained and the dynamics of localized waves are analyzed via numerical simulation plots
Summary
Most nonlinear partial differential equations (PDEs) in mathematics and physics are integrable, including the Hirota equation [1], the nonlinear Schrödinger equation [2, 3], the Gerdjikov-Ivanov equation [4], the Korteweg-de Vries equation [5, 6], the Sasa-Satsuma equation [7], and so on. These nonlinear equations play an important role in various fields of nonlinear science such as water waves, nonlinear optics, and Bose-Einstein condensates. Journal of Nonlinear Mathematical Physics (2022) 29:318–330 researchers than the single-component system [8, 9] These nonlinear equations can be used to describe and study localized waves, which consist of rogue waves [10, 11], solitons [12, 13], and breathers [14–17].
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