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Article
The Defocusing Nonlinear Schrödinger Equation with a Nonzero Background: Painlevé Asymptotics in Two Transition Regions
In this paper, we address the Painlevé asymptotics of the solution in two transition regions for the defocusing nonlinear Schrödinger (NLS) equation with finite density initial data
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Long Time Asymptotics Behavior of the Focusing Nonlinear Kundu-Eckhaus Equation
The authors study the Cauchy problem for the focusing nonlinear Kundu-Eckhaus (KE for short) equation and construct the long time asymptotic expansion of its solution in fixed space-time cone with C(x1, x2, v1, v
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Long Time Asymptotic Behavior for the Nonlocal mKdV Equation in Solitonic Space–Time Regions
We study the long time asymptotic behavior for the Cauchy problem of an integrable real nonlocal mKdV equation with nonzero initial data in the solitonic regions
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Article
Long-time Asymptotic Behavior for the Derivative Schrödinger Equation with Finite Density Type Initial Data
In this paper, the authors apply \(\overline \partial \) steepest descent method to study the Cauchy problem for the derivative...
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Article
Inverse scattering transform and multiple high-order pole solutions for the Gerdjikov–Ivanov equation under the zero/nonzero background
In this article, the inverse scattering transform is considered for the Gerdjikov–Ivanov equation with zero and non-zero boundary conditions by a matrix Riemann–Hilbert (RH) method. The formula of the soliton ...
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Article
Open AccessThe (N + 1)-Dimensional Burgers Equation: A Bilinear Extension, Vortex, Fusion and Rational Solutions
In this paper, by introducing a fractional transformation, we obtain a bilinear formulation for the (N + 1)-dimensional Burgers equation. Such a formulation constitutes a bilinear extension to the (N + 1)-dimensi...
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Article
Open AccessInverse Scattering Transformation for the Fokas–Lenells Equation with Nonzero Boundary Conditions
In this article, we focus on the inverse scattering transformation for the Fokas–Lenells (FL) equation with nonzero boundary conditions via the Riemann–Hilbert (RH) approach. Based on the Lax pair of the FL eq...
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Article
Rogue wave and multi-pole solutions for the focusing Kundu–Eckhaus Equation with nonzero background via Riemann–Hilbert problem method
In this work, we use the inverse scattering transform method to consider the focusing Kundu–Eckhaus (KE) equation with nonzero background (NZBG) at infinity. Based on the analytical, symmetric, asymptotic prop...
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Article
Inverse scattering transform for the Gerdjikov–Ivanov equation with nonzero boundary conditions
In this article, we focus on the inverse scattering transform for the Gerdjikov–Ivanov equation with nonzero boundary at infinity. An appropriate two-sheeted Riemann surface is introduced to map the original s...
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Article
Long-Time Asymptotic Behavior for the Discrete Defocusing mKdV Equation
In this article, we apply Deift–Zhou nonlinear steepest descent method to analyze the long-time asymptotic behavior of the solution for the discrete defocusing mKdV equation $$\begin{aligned} \dot{q}_n = \left( 1...
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Article
N-Soliton Solution of The Kundu-Type Equation Via Riemann-Hilbert Approach
In this article, we focus on investigating the Kundu-type equation with zero boundary condition at infinity. Based on the analytical and symmetric properties of eigenfunctions and spectral matrix of its Lax pa...
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Whitham Hierarchy and Generalized Picard–Fuchs Operators in the N=2 Susy Yang–Mills Theory for Classical Gauge Groups
We derive infinitely many meromorphic differentials based on the fractional powers of the superpotential arising from hyperelliptic curves. We obtain various differential equations expressed in terms of the mo...
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Article
Open AccessQuasiperiodic Solutions of the Heisenberg Ferromagnet Hierarchy
We present quasi-periodic solutions in terms of Riemann theta functions of the Heisenberg ferromagnet hierarchy by using algebro-geometric method. Our main tools include algebraic curve and Riemann surface, po...
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Article
BRST Formalism in Self-Dual Chern-Simons Theory with Matter Fields
We apply BRST method to the self-dual Chern-Simons gauge theory with matter fields and the generators of symmetries of the system from an elegant Lie algebra structure under the operation of Poisson bracket. W...
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Article
Open AccessInitial-boundary value problem for the two-component Gerdjikov-Ivanov equation on the interval
In this paper, we apply Fokas unified method to study initial-boundary value problems for the two-component Gerdjikov-Ivanov equation formulated on the finite interval with 3 × 3 Lax pairs. The solution can be...
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Article
The Initial-boundary Value Problem for the Ostrovsky-Vakhnenko Equation on the Half-line
We analyze an initial-boundary value problem for the Ostrovsky-Vakhnenko equation on the half-line. This equation can be viewed as the short wave model for the Degasperis-Procesi (DP) equation. We show that th...
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A Riemann-Hilbert approach to the Harry-Dym equation on the line
In this paper, the authors consider the Harry-Dym equation on the line with decaying initial value. They construct the solution of the Harry-Dym equation via the solution of a 2 × 2 matrix Riemann-Hilbert prob...
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Article
Algebro-geometric Solutions for the Derivative Burgers Hierarchy
Though completely integrable Camassa–Holm (CH) equation and Degasperis–Procesi (DP) equation are cast in the same peakon family, they possess the second- and third-order Lax operators, respectively. From the v...
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Article
Open AccessAlgebro-geometric solutions for the two-component Hunter-Saxton hierarchy
This paper is dedicated to provide theta function representations of algebro-geometric solutions and related crucial quantities for the two-component Hunter-Saxton (HS2) hierarchy through an algebro-geometric ...
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Article
Algebro-geometric solutions for the Hunter–Saxton hierarchy
This paper is dedicated to provide theta function representations of algebro-geometric solutions and related crucial quantities for the Hunter–Saxton (HS) hierarchy through studying an algebro-geometric initia...
