The Darboux transformation of the derivative nonlinear Schrödinger equation
By Shuwei Xu, Jingsong He, Lihong Wang. 2011
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The n-fold Darboux transformation (DT) is a 2 × 2 matrix for the Kaup–Newell (KN) system. In this paper, each element of this matrix is expressed by a ratio of the (n + 1) × (n + 1) determinant and n × n determinant of eigenfunctions. Using these formulae, the expressions of the q[n] and r[n] in the KN system are generated by the n-fold DT. Further, under the reduction condition, the rogue wave, rational traveling solution, dark soliton, bright soliton, breather solution and periodic solution of the derivative nonlinear Schrödinger equation are given explicitly by different seed solutions. In particular, the rogue wave and rational traveling solution are two kinds of new solutions. The complete classification of these solutions generated by one-fold DT is given.
Subfields: Modeling and Simulation, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/45d738db89b83219e66fdedaf6d30d0acd253174
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In Modeling and Simulation
In Statistical and Nonlinear Physics
Citations in the corpus
- Dynamics of rogue waves in the Davey–Stewartson II equation (2012, background): “Ik (Some figures may appear in colour only in the online journal)”