Nondegenerate soliton dynamics of nonlocal nonlinear Schrödinger equation

Geng, Kai-Li; Zhu, Bo-Wei; Cao, Qi-Hao; Dai, Chao-Qing; Wang, Yueyue

doi:10.1007/s11071-023-08719-w

Cited by 67 publications

(8 citation statements)

References 45 publications

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“…( 2) is at least up to O(1/ε 2 ) according to the research for the nonlinear Klein-Gordon equation provided with the cubic nonlinearlity [22,23]. Note that the long-time dynamics of the NSFSGE (1) is equivalent to that of the NSFSGE (2). Then we only discuss the error estimation of the long-time dynamics for the NSFSGE (2) with weak nonlinearity at time O(1/ε 2 ) and the relevant conclusions can be easily generalized to Eq.…”

Section: Introductionmentioning

confidence: 95%

“…Nonlinear wave equations and their dynamic properties explain the rich and colorful natural phenomena reasonably, such as the wave propagation, smooth scattering, emission and absorption in electromagnetism, superelastic material [1][2][3][4]. Some well-known nonlinear wave equations are Schrödinger equations, Klein-Gordon equations, sine-Gordon equations, Korteweg-deVries equation, Burgers equation and so on.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Improved Uniform Error Bounds of Exponential Wave Integrator Method for Long-Time Dynamics of the Space Fractional Klein-Gordon Equation with Weak Nonlinearity

Jia,

Jiang

2023

J Sci Comput

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In this paper, we derive the improved uniform error bounds for the long-time dynamics of the d-dimensional (d = 2, 3) nonlinear space fractional sine-Gordon equation (NSFSGE). The nonlinearity strength of the NSFSGE is characterized by ε 2 where 0 < ε ≤ 1 is a dimensionless parameter. The second-order time-splitting method is applied to the temporal discretization and the Fourier pseudo-spectral method is used for the spatial discretization. To obtain the explicit relation between the numerical errors and the parameter ε, we introduce the regularity compensation oscillation technique to the convergence analysis of fractional models. Then we establish the improved uniform error bounds O ε 2 τ 2 for the semi-discretization scheme and O h m + ε 2 τ 2 for the full-discretization scheme up to the long time at O(1/ε 2 ). Further, we extend the time-splitting Fourier pseudo-spectral method to the complex NSFSGE as well as the oscillatory complex NSFSGE, and the improved uniform error bounds for them are also given. Finally, extensive numerical examples in two-dimension or three-dimension are provided to support the theoretical analysis. The differences in dynamic behaviors between the fractional sine-Gordon equation and classical sine-Gordon equation are also discussed.

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Section: Introductionmentioning

confidence: 95%

Section: Introductionmentioning

confidence: 99%

Improved Uniform Error Bounds of Exponential Wave Integrator Method for Long-Time Dynamics of the Space Fractional Klein-Gordon Equation with Weak Nonlinearity

Jia,

Jiang

2023

J Sci Comput

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“…To thoroughly analyze the propagation of solitons in such systems, researchers often turn to the nonlinear Schrödinger equation, which effectively captures the simultaneous evolution of multiple classes of solitons. [19][20][21] Among these equations, the coupled nonlinear Schrödinger (CNLS) equation stands out, drawing considerable interest in the realms of mathematics and physics. This is due to its ability to support two-component fundamental modes under various optical conditions.…”

Section: Introductionmentioning

confidence: 99%

Compression and stretching of ring vortex in a bulk nonlinear medium

Lai 来,

Cai 蔡,

Shao 邵

et al. 2024

Chinese Phys. B

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We explore the nonlinear gain coupled Schrödinger system through the utilization of the variables separation method and ansatz technique. By employing these approaches, we generate hierarchies of explicit dissipative vector vortices (DVVs) that possess diverse vorticity values. Numerous fundamental characteristics of the DVVs are examined, encompassing amplitude profiles, energy fluxes, parameter effects, as well as linear and dynamic stability.

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“…Therefore, research of the exact solutions of NLEEs with a variety of physical models is of great significance. [4][5][6][7][8] Through the concerted efforts of many researchers, many effective methods have been developed, such as the Hirota bilinear method, [9][10][11] the Lie symmetry analysis method, [12] the Riemann-Hilbert method, [13,14] neural network method, [15] and the Darboux transformation. [16][17][18] The Darboux transformation is a canonical transformation of the spectral problem for NLEEs.…”

Section: Introductionmentioning

confidence: 99%

Darboux transformation, infinite conservation laws, and exact solutions for the nonlocal Hirota equation with variable coefficients

Liu 刘,

Yan 闫,

Jin 金

et al. 2023

Chinese Phys. B

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This article presents the construction of a nonlocal Hirota equation with variable coefficient and its Darboux transformation. Using zero-seed solutions, 1-soliton and 2-soliton solutions of the equation are constructed through the Darboux transformation, along with the expression for N-soliton solutions. The influence of coefficient functions on the solutions is investigated by choosing different coefficient functions, and the dynamics of the solutions are analyzed. For the first time, this article utilizes the Lax pair to construct infinite conservation laws and extends it to nonlocal equations. The study of infinite conservation laws for nonlocal equations holds significant implications for the integrability of nonlocal equations.

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Nondegenerate soliton dynamics of nonlocal nonlinear Schrödinger equation

Cited by 67 publications

References 45 publications

Improved Uniform Error Bounds of Exponential Wave Integrator Method for Long-Time Dynamics of the Space Fractional Klein-Gordon Equation with Weak Nonlinearity

Improved Uniform Error Bounds of Exponential Wave Integrator Method for Long-Time Dynamics of the Space Fractional Klein-Gordon Equation with Weak Nonlinearity

Compression and stretching of ring vortex in a bulk nonlinear medium

Darboux transformation, infinite conservation laws, and exact solutions for the nonlocal Hirota equation with variable coefficients

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