On the basis of the spectral analysis of the 4 * 4 4× 4 Lax pair associated with the spin-1
Gross–Pitaevskii equation and the scattering matrix, the solution to the Cauchy problem of …

The complete classification of solutions to the defocusing complex modified KdV equation
with step-like initial condition is studied by the finite-gap integration approach and Whitham …

We present an application of the nonlinear steepest descent method to a three-component
coupled mKdV system associated with a 4× 4 matrix spectral problem. An integrable …

Starting from a specific example of 4× 4 matrix spectral problems, an integrable coupled
hierarchy, which includes a three-component coupled nonlinear Schrödinger system as the …

The mathematical description of localized solitons in the presence of large‐scale waves is a
fundamental problem in nonlinear science, with applications in fluid dynamics, nonlinear …

The long-time asymptotic behavior of solutions to the focusing nonlinear Schrödinger (NLS)
equation on the line with symmetric, nonzero boundary conditions at infinity is studied in the …

In this paper, we study the Cauchy problem of the positive flow short-pulse equation by
using the Riemann–Hilbert approach, from which we obtain multi-soliton formulas of the …

We study the Cauchy problem for the integrable nonlocal focusing nonlinear Schrödinger
(NNLS) equation iq_ t (x, t)+ q_ xx (x, t)+ 2 q^ 2 (x, t) ̄ q (-x, t)= 0 iqt (x, t)+ q xx (x, t)+ 2 q 2 (x …

We address two pressing questions in the theory of the Korteweg–de Vries (KdV) equation.
First, we show the uniqueness of solutions to KdV that are merely bounded, without any …

On the basis of the inverse scattering transformation, the Cauchy problem of the coupled
modified Korteweg–de Vries equation is transformed to a 3× 3 matrix Riemann–Hilbert …