138 citations · 583 across the 12 of their papers we have counts for
12 papers
Traveling periodic waves and breathers in the nonlocal derivative NLS equation
Jinbing Chen, Dmitry E. Pelinovsky
A nonlocal derivative NLS (nonlinear Schrödinger) equation describes modulations of waves in a stratified fluid and a continuous limit of the Calogero--Moser--Sutherland system of…
Bright and dark breathers of the Benjamin-Ono equation on the traveling periodic background
Jinbing Chen, Dmitry E. Pelinovsky
The Benjamin-Ono (BO) equation describes long internal waves of small amplitude in deep fluids. Compared to its counterpart for shallow fluids, the Korteweg-de Vries (KdV) equation…
Rogue waves arising on the standing periodic waves in the Ablowitz-Ladik equation
Jinbing Chen, Dmitry E. Pelinovsky
We study the standing periodic waves in the semi-discrete integrable system modelled by the Ablowitz-Ladik equation. We have related the stability spectrum to the Lax spectrum by s…
Rogue waves on the background of periodic standing waves in the derivative NLS equation
Jinbing Chen, Dmitry E. Pelinovsky
The derivative nonlinear Schrodinger (DNLS) equation is the canonical model for dynamics of nonlinear waves in plasma physics and optics. We study exact solutions describing rogue…
Modulational instability of periodic standing waves in the derivative NLS equation
Jinbing Chen, Dmitry E. Pelinovsky, Jeremy Upsal
We consider the periodic standing waves in the derivative nonlinear Schrodinger (DNLS) equation arising in plasma physics. By using a newly developed algebraic method with two eige…
Rogue waves on the double-periodic background in the focusing nonlinear Schrodinger equation
Jinbing Chen, Dmitry E. Pelinovsky, Robert E. White
The double-periodic solutions of the focusing nonlinear Schrodinger equation have been previously obtained by the method of separation of variables. We construct these solutions by…
Quasi-periodic solutions to the negative-order KdV hierarchy
Jinbing Chen
A complete algorithm is developed to deduce quasi-periodic solutions for the negative-order KdV (nKdV) hierarchy by using the backward Neumann systems. From the nonlinearization of…
Rogue waves on the periodic wave background in the focusing nonlinear Schrodinger equation
Jinbing Chen, Dmitry E. Pelinovsky, Robert E. White
We present exact solutions for rogue waves arising on the background of periodic waves in the focusing nonlinear Schrodinger equation. The exact solutions are obtained by character…
Periodic travelling waves of the modified KdV equation and rogue waves on the periodic background
Jinbing Chen, Dmitry E. Pelinovsky
We address the most general periodic travelling wave of the modified Korteweg-de Vries (mKdV) equation written as a rational function of Jacobian elliptic functions. By applying an…
Rogue periodic waves of the focusing NLS equation
Jinbing Chen, Dmitry E. Pelinovsky
Rogue waves on the periodic background are considered for the nonlinear Schrodinger (NLS) equation in the focusing case. The two periodic wave solutions are expressed by the Jacobi…
Neumann Type Integrable Reduction to the Negative-Order Coupled Harry--Dym Hierarchy
Jinbing Chen
Based on the Lax compatibility, the negative-order coupled Harry--Dym (ncHD) hierarchy depending upon one parameter is retrieved in the Lenard scheme, which includes the two-co…
Rogue periodic waves of the mKdV equation
Jinbing Chen, Dmitry E. Pelinovsky
Traveling periodic waves of the modified Korteweg-de Vries (mKdV) equation are considered in the focusing case. By using one-fold and two-fold Darboux transformations, we construct…