Rogue waves in the generalized derivative nonlinear Schrodinger equations

Yang, Bo; Chen, Junchao; Yang, Jianke

doi:10.48550/arxiv.1912.05589

Cited by 1 publication

(3 citation statements)

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“…It also reproduces f 1 (p) = ±p for the NLS equation in [29] and f 1 (p) = ±(p + iα) for the generalized derivative NLS equations in [57]. Notice that even though Q 1 (p 0 ) = 0, f 1 (p) still has a limit when p → p 0 , and hence f 1 (p 0 ) is well-defined.…”

Section: A Simple Rootsupporting

confidence: 54%

“…However, applying the method as used for the generalized derivative NLS equations in [57], we can show that all evenindexed parameters a even are dummy parameters which cancel out automatically from the solution. Thus, we will set a 2 = a 4 = • • • = a even = 0 throughout this article.…”

Section: B Rogue Wave Solutionsmentioning

confidence: 99%

“…Now, it is time to introduce free parameters into these rational solutions. As we did previously for the derivative NLS equations in [57], we will introduce these free parameters through the arbitrary constant ξ 0 in Eq. (83).…”

Section: Introduction Of Free Parametersmentioning

confidence: 99%

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General rogue waves in the three-wave resonant interaction systems

Yang

2021

IMA Journal of Applied Mathematics

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General rogue waves in (1+1)-dimensional three-wave resonant interaction systems are derived by the bilinear method. These solutions are divided into three families, which correspond to a simple root, two simple roots and a double root of a certain quartic equation arising from the dimension reduction, respectively. It is shown that while the first family of solutions associated with a simple root exists for all signs of the nonlinear coefficients in the three-wave interaction equations, the other two families of solutions associated with two simple roots and a double root can only exist in the so-called soliton-exchange case, where the nonlinear coefficients have certain signs. Many of these rogue wave solutions, such as those associated with two simple roots, the ones generated by a $2\times 2$ block determinant in the double-root case, and higher-order solutions associated with a simple root, are new solutions which have not been reported before. Technically, our bilinear derivation of rogue waves for the double-root case is achieved by a generalization to the previous dimension reduction procedure in the bilinear method, and this generalized procedure allows us to treat roots of arbitrary multiplicities. Dynamics of the derived rogue waves is also examined, and new rogue wave patterns are presented. Connection between these bilinear rogue waves and those derived earlier by Darboux transformation is also explained.

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Section: A Simple Rootsupporting

confidence: 54%

Section: B Rogue Wave Solutionsmentioning

confidence: 99%