Breather and nondegenerate solitons in the two-component modified Korteweg-de Vries equation

Article Mathematics, Applied

Long-time asymptotic behavior for the matrix modified Korteweg-de Vries equation

Nan Liu et al.

Summary: The long-time asymptotics of solution to the integrable matrix modified Korteweg-de Vries equation with a 4 x 4 Lax pair on the line in the case of decaying initial data is established. The (x, t)-plane mainly decomposes asymptotically in time into three types of regions: a left oscillating region, a central Painleve region, and a right fast decaying region. The study makes use of the inverse scattering transform and the nonlinear steepest descent method for oscillatory Riemann-Hilbert problems.

PHYSICA D-NONLINEAR PHENOMENA (2023)

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Article Mathematics, Applied

N-soliton solutions for the coupled extended modified KdV equations via Riemann-Hilbert approach

Fan Wu et al.

Summary: In this paper, the Riemann-Hilbert method is used to construct the N-soliton solutions for the coupled extended modified KdV equations with zero boundary condition. The relationship between the solutions of the coupled extended modified KdV equations and a Riemann-Hilbert problem is established. By solving a particular Riemann-Hilbert problem with an identity jump matrix, the general N-soliton solutions of the coupled extended modified KdV equations are derived. The local structures of the N-soliton solution are also graphically presented by choosing parameters suitably.

APPLIED MATHEMATICS LETTERS (2022)

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Article Physics, Fluids & Plasmas

Dynamics of nondegenerate vector solitons in a long-wave-short-wave resonance interaction system

S. Stalin et al.

Summary: In this paper, the authors study the dynamics of a class of interesting vector solitons in the long-wave-short-wave resonance interaction system. They derive nondegenerate vector soliton solutions using the Hirota bilinear method and express the solutions in a compact form using Gram-determinants. The authors also analyze the collision scenarios of the solitons and point out the shape-changing behavior of the nondegenerate solitons, which has not been observed in the already known vector solitons.

PHYSICAL REVIEW E (2022)

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Article Mathematics, Applied

A two-component modified Korteweg-de Vries equation: Riemann-Hilbert problem and multi-soliton solutions

Xue-Wei Yan

Summary: This paper investigates the inverse scattering transform of a two-component modified Korteweg-de Vries equation, obtaining multi-soliton solutions through spectral analysis and a Riemann-Hilbert formulation. Figures are presented to demonstrate the soliton features of the equation.

INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS (2021)

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Article Mathematics, Interdisciplinary Applications

Vector bright soliton interactions of the two-component AB system in a baroclinic fluid

Cui-Cui Ding et al.

Summary: This paper investigates a two-component AB system describing wave-packets in a baroclinic fluid. Bright one- and two-soliton solutions are constructed, and the effects of coefficients on the wave packets are analyzed, revealing the interactions between different types of solitons.

CHAOS SOLITONS & FRACTALS (2021)

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Article Physics, Fluids & Plasmas