N-fold Darboux transformation and exact solutions for the nonlocal Fokas–Lenells equation on the vanishing and plane wave backgrounds
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Li Li
Abstract
In this paper, we propose and investigate the reverse-space–time nonlocal nonlinear Fokas–Lenells equation by the idea of Ablowitz and Musslimani. The reverse-space–time Fokas–Lenells equation, associated with a 2 × 2 matrix Lax pair, is the important integrable system, which can be reduced to the nonlocal Fokas–Lenells equation. Based on its Lax pair, we construct nonlocal version of N-fold Darboux transformation (DT) for the Fokas–Lenells equation, and obtain two kinds of soliton solutions from vanishing and plane wave backgrounds. Further some novel one-soliton and two-soliton are derived with the zero and nonzero seed solutions through complex computations, including the bright soliton, kink soliton and breather wave soliton. Moreover, various graphical analyses on the presented solutions are made to reveal the dynamic behaviors, which display the elastic interactions between two solitons and their amplitudes keeping unchanged after the interactions except for the phase shifts. It is clearly shown that these solutions have new properties which differ from ones of the classical Fokas–Lenells equation.
Funding source: The scientific research funding projects of department education of Liaoning province
Award Identifier / Grant number: LJKZ01007
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Author contribution: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.
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Research funding: This work was sponsored by the scientific research funding projects of department education of Liaoning province, China (Grant No. LJKZ01007) and Liaoning Baiqianwan Talents Program (Grant No. 2019921075).
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Conflict of interest statement: The authors declare that they have no conflict of interest.
References
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© 2022 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- Original Research Articles
- One-dimensional optimal system and similarity transformations for the 3 + 1 Kudryashov–Sinelshchikov equation
- Hopf bifurcations in a network of FitzHugh–Nagumo biological neurons
- Gravity modulation effect on weakly nonlinear thermal convection in a fluid layer bounded by rigid boundaries
- A new numerical formulation for the generalized time-fractional Benjamin Bona Mohany Burgers’ equation
- Chebyshev spectral method for solving a class of local and nonlocal elliptic boundary value problems
- Adaptive extragradient methods for solving variational inequalities in real Hilbert spaces
- Elastic trend filtering
- A new approach to representations of homothetic motions in Lorentz space
- Numerical simulation of variable-order fractional differential equation of nonlinear Lane–Emden type appearing in astrophysics
- Stability analysis and numerical simulations of the fractional COVID-19 pandemic model
- Numerical solutions of the Bagley–Torvik equation by using generalized functions with fractional powers of Laguerre polynomials
- N-fold Darboux transformation and exact solutions for the nonlocal Fokas–Lenells equation on the vanishing and plane wave backgrounds
- Closed form soliton solutions to the space-time fractional foam drainage equation and coupled mKdV evolution equations
- Master-slave synchronization in the Duffing-van der Pol and Φ6 Duffing oscillators
- Singularity analysis and analytic solutions for the Benney–Gjevik equations
- Trajectory controllability of nonlinear fractional Langevin systems
- Similarity transformations for modified shallow water equations with density dependence on the average temperature
- Non-equidistant partition predictor–corrector method for fractional differential equations with exponential memory
- Dynamical analysis of fractional-order of IVGTT glucose–insulin interaction
- Dynamic response of Mathieu–Duffing oscillator with Caputo derivative
- Non-Newtonian fluid flow having fluid–particle interaction through a porous zone in a channel with permeable walls
- A class of computationally efficient Newton-like methods with frozen inverse operator for nonlinear systems
Articles in the same Issue
- Frontmatter
- Original Research Articles
- One-dimensional optimal system and similarity transformations for the 3 + 1 Kudryashov–Sinelshchikov equation
- Hopf bifurcations in a network of FitzHugh–Nagumo biological neurons
- Gravity modulation effect on weakly nonlinear thermal convection in a fluid layer bounded by rigid boundaries
- A new numerical formulation for the generalized time-fractional Benjamin Bona Mohany Burgers’ equation
- Chebyshev spectral method for solving a class of local and nonlocal elliptic boundary value problems
- Adaptive extragradient methods for solving variational inequalities in real Hilbert spaces
- Elastic trend filtering
- A new approach to representations of homothetic motions in Lorentz space
- Numerical simulation of variable-order fractional differential equation of nonlinear Lane–Emden type appearing in astrophysics
- Stability analysis and numerical simulations of the fractional COVID-19 pandemic model
- Numerical solutions of the Bagley–Torvik equation by using generalized functions with fractional powers of Laguerre polynomials
- N-fold Darboux transformation and exact solutions for the nonlocal Fokas–Lenells equation on the vanishing and plane wave backgrounds
- Closed form soliton solutions to the space-time fractional foam drainage equation and coupled mKdV evolution equations
- Master-slave synchronization in the Duffing-van der Pol and Φ6 Duffing oscillators
- Singularity analysis and analytic solutions for the Benney–Gjevik equations
- Trajectory controllability of nonlinear fractional Langevin systems
- Similarity transformations for modified shallow water equations with density dependence on the average temperature
- Non-equidistant partition predictor–corrector method for fractional differential equations with exponential memory
- Dynamical analysis of fractional-order of IVGTT glucose–insulin interaction
- Dynamic response of Mathieu–Duffing oscillator with Caputo derivative
- Non-Newtonian fluid flow having fluid–particle interaction through a porous zone in a channel with permeable walls
- A class of computationally efficient Newton-like methods with frozen inverse operator for nonlinear systems
