A Riemann-Hilbert approach to the Kundu-nonlinear Schrödinger equation and its multi-component generalization

Li, Jian; Xia, Tiecheng

doi:10.1016/j.jmaa.2021.125109

Cited by 29 publications

(11 citation statements)

References 20 publications

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“…In this paper, according to the Riemann-Hilbert method, the N -soliton of the cSTO equation can be constructed. And the next step is to try to generalize the cSTO equation in multiple components, such as the multi-component generalization of the Kundu-NLS equation [23]. In fact, the cSTO equation is a kind of significant equation in mathematical physics, so it is very meaningful to do something similar to the STO equation.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

Riemann–Hilbert approach of the complex Sharma–Tasso–Olver equation and its N-soliton solutions

Xia

Wei

2023

Chinese Phys. B

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In this paper, we study the complex Sharma-Tasso-Olver equation via the Riemann-Hilbert approach. The associated Riemann-Hilbert problem for this integrable equation can be naturally constructed by considering the spectral problem of the Lax pair. Subsequently, in the case where the Riemann-Hilbert problem is irregular, the N-soliton solutions of the equation can be deduced. In addition, the three-dimensional graphic of the soliton solutions and wave propagation image are graphically depicted and further discussed.

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Section: Conclusion and Discussionmentioning

confidence: 99%

Riemann–Hilbert approach of the complex Sharma–Tasso–Olver equation and its N-soliton solutions

Xia

Wei

2023

Chinese Phys. B

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“…These solutions can further help to understand natural phenomena and laws. In recent years, more and more mathematical physicists have begun to pay attention to Riemann-Hilbert (RH) approach [9,10], which is a new powerful method for solving integrable linear and nonlinear evolution equations [11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]. The main idea of this method is to establish a corresponding matrix RH problem on the Lax pair of integrable equations.…”

Section: Introductionmentioning

confidence: 99%

Dynamic behaviors of soliton solutions for a three-coupled Lakshmanan–Porsezian–Daniel model

Lin

Zhang

2022

Nonlinear Dyn

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In this paper, we use the Riemann-Hilbert (RH) approach to examine the integrable three-coupled Lakshmanan-Porsezian-Daniel (LPD) model, which describe the dynamics of alpha helical protein with the interspine coupling at the fourth-order dispersion term. Through the spectral analysis of Lax pair, we construct the higher order matrix RH problem for the three-coupled LPD model, when the jump matrix of this particular RH problem is a 4 × 4 unit matrix, the exact N-soliton solutions of the three-coupled LPD model can be exhibited. As special examples, we also investigate the nonlinear dynamical behaviors of the single-soliton, two-soliton, three-soliton and breather soliton solutions. Finally, an integrable generalized N-component LPD model with its linear spectral problem is discussed.

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“…Explicit solutions of an integrable equation are difficult to obtain usually. In order to find explicit solutions of integrable equation, some useful approaches have been proposed, such as algebraic-geometry method, 16 Riemann-Hilbert method, 17 Bäcklund transformation, 18 and Darboux transformation. [19][20][21][22][23] In these methods, Darboux transformation is a very effective tool to generate explicit solutions of integrable equation.…”

Section: Introductionmentioning

confidence: 99%

Liouville integrability and explicit solutions for a Frobenius‐coupled integrable lattice hierarchy

Yang

2022

Math Methods in App Sciences

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We define a Frobenius-coupled integrable lattice hierarchy including its Lax pair.Then the bi-Hamiltonian structures of this hierarchy are constructed, which show that this hierarchy possesses Liouville integrability. We also obtained N-fold Darboux transformation of the Frobenius-coupled integrable lattice hierarchy. Finally, the explicit solutions after onefold Darboux transformation of this hierarchy are investigated when we choose appropriate seed solutions.

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A Riemann-Hilbert approach to the Kundu-nonlinear Schrödinger equation and its multi-component generalization

Cited by 29 publications

References 20 publications

Riemann–Hilbert approach of the complex Sharma–Tasso–Olver equation and its N-soliton solutions

Riemann–Hilbert approach of the complex Sharma–Tasso–Olver equation and its N-soliton solutions

Dynamic behaviors of soliton solutions for a three-coupled Lakshmanan–Porsezian–Daniel model

Liouville integrability and explicit solutions for a Frobenius‐coupled integrable lattice hierarchy

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