Nonlinear Waves in Integrable and Nonintegrable Systems

By Jianke Yang. Mathematical modeling and computation, 2010

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Nonlinear Fourier Transform for Optical Data Processing and Transmission: Advances and Perspectives (2017, methodology): “, [43] and references therein), and numerical solution of the NFT can be implemented using this approach [132].”
Stability analysis for solitons in PT-symmetric optical lattices (2012, methodology): “A notable difference is that for real potentials, real eigenvalues bifurcate out of the origin exactly at the minimum of the power curve [17], whereas here this real-eigenvalue bifurcation occurs not at the power minimum.”
(INVITED) Vortex solitons: Old results and new perspectives (2019, background): “Note that the defocusing nonlinearity may create gap solitons in the presence of the lattice potential [5, 7, 176].”
Transformations between Nonlocal and Local Integrable Equations (2017, methodology): “For instance, using the first four conserved quantities of the local NLS equation [5], we immediately obtain the first four conserved quantities of the reverse-time nonlinear diffusion”
Long-time asymptotics for the nonlocal nonlinear Schrödinger equation with step-like initial data (2021, methodology): “1a) were found using the Hirota’s direct method and the Riemann-Hilbert approach respectively (see also [37], where the N-soliton solution of the general coupled Schrödinger equations (1.”