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Darboux transformation and solitonic solution to the coupled complex short pulse equation
Bao-Feng Feng, Liming Ling
The Darboux transformation (DT) for the coupled complex short pulse (CCSP) equation is constructed through the loop group method. The DT is then utilized to construct various exact…
Measuring the rogue wave pattern triggered from Gaussian perturbations by deep learning
Liwen Zou, XinHang Luo, Delu Zeng +2
Weak Gaussian perturbations on a plane wave background could trigger lots of rogue waves, due to modulational instability. Numerical simulations showed that these rogue waves seeme…
Stability of elliptic function solutions for the focusing modified KdV equation
Liming Ling, Xuan Sun
We study the spectral and orbital stability of elliptic function solutions for the focusing modified Korteweg-de Vries (mKdV) equation and construct the corresponding breather solu…
Kadomtsev-Petviashvili equation: one-constraint method and lump pattern
Jie-Yang Dong, Liming Ling, Xiaoen Zhang
The Kadomtsev-Petviashvili reduction method is a crucial method to derive the solitonic solutions of (1+1) dimensional integrable system from high dimensional system. In this work,…
Large and infinite order solitons of the coupled nonlinear Schrödinger equation
Liming Ling, Xiaoen Zhang
We study the large order and infinite order soliton of the coupled nonlinear Schrodinger equation with the Riemann-Hilbert method. By using the Riemann-Hilbert representation for t…
Multivalley dark solitons in multicomponent Bose-Einstein condensates with repulsive interactions
Yan-Hong Qin, Li-Chen Zhao, Zeng-Qiang Yang +1
We obtain multivalley dark soliton solutions with asymmetric or symmetric profiles in multicomponent repulsive Bose-Einstein condensates by developing the Darboux transformation me…